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1 Basic Vehicle Motion Analysis: A Modern Accident Reconstruction Guide
mil
es
ho
ur
1.4
67
speed = = 52.4
4.16 Tasks that Yield Speed when a
Vehicle Decelerates from One Speed to a
Slower Speed
A. Final speed when initial speed, distance traveled
and deceleration time are known (task 40-40!
Example:
1. A vehicle is traveling at 50.0 miles per hour.
2.he vehicle decelerates covering a distance o! "50.0
!eet in 5.0 seconds.
3. #hat is the speed o! the vehicle a!ter deceleration$
%olution:
2 x distance . . . &speed = '''''''' ' initial speed
time x 1.46
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mil
es
ho
ur
1.4
67
speed = = 52.4
7
B. Final speed when initial speed, distance traveledand deceleration are known (task 40-40"!
Example:
1. A vehicle is traveling at 55.0 miles per hour.
2. he vehicle decelerates at ".0 !eet per second per
second covering a distance o! 100.0 !eet.
3. #hat is the speed o! the vehicle a!ter deceleration$
%olution:
( )*+initial speed x 1.467,2 ' +2 x
deceleration x distance, spee ' 1.467
C. Final speed when initial speed, distance traveledand dra# factor are known (task 40-40$!
Example:
2 x "50.0 !eet5.0 seconds x
1.467
speed= hou
r
50.0 ) = 45.4 -le%
hour
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" Basic Vehicle Motion Analysis: A Modern Accident Reconstruction Guide
mil
es
ho
ur
1.4
67
speed = = 52.4
1. A vehicle is traveling at 55.0 miles per hour.
2. he vehicle decelerates ith a drag !actor o! 0.15
covering a distance o! 100.0 !eet.
3. #hat is the speed o! the vehicle a!ter deceleration$
%olution:
speed =
1.467
speed = 50./
D. Final speed when initial speed, deceleration timeand deceleration are known (task 40-404!
Example:
1. A vehicle is traveling at 55.0 miles per hour.
2. he vehicle decelerates at ".0 !eet per second per
!eet
second2
2 x drag !actor x"2.2
xdistance
+initial speed x1.467,
2 '
!eet
x 100.0
!eet
2 x 0.15
x"2.2
secon
dspeed= 1.4
67
(( miles &
55.0 ' ' x1.467
hour
miles
hour
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mil
es
ho
ur
1.4
67
speed = = 52.4
second !or a duration o! /.0 seconds.
3. #hat is the speed o! the vehicle a!ter deceleration$
%olution:
deceleration x time
1.46
7
E. Final speed wheninitial speed,deceleration time and dra# factor are known(task 40-40%!
Example:
1. A vehicle is traveling at 55.0 miles per hour.
2. he vehicle decelerates ith a drag !actor o! 0.15 !or
a duration o! /.0 seconds.
3. #hat is the speed o! the vehicle a!ter deceleration$
speed = initialspeed '
!eetsecond2
".0
x /.0 seconds
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5 Basic Vehicle Motion Analysis: A Modern Accident Reconstruction Guide
mil
es
ho
ur
1.4
67
speed = = 52.4
%olution:
!eet
drag !actor x "2.2 x time
second
F. &nitial speed when 'nal speed, distance traveledand deceleration time are known (task 40-40!
Example:
1. A vehicle is traveling at an unnon speed.
2. he vehicle decelerates covering a distance o!
"50.0 !eet in 5.0 seconds& reaching a 3nal speed o! "0.0
miles per hour.
3. #hat as the speed o! the vehicle e!ore
speed = initialspeed
0.15 x
"2.2
x /.0
seconds
mile
s
hour
mile
s
hour
speed= 55.0 =2/.7
1.4
67! eet
second1.467
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mil
es
ho
ur
1.4
67
speed = = 52.4
deceleration$
%olution:
& 2 xdistance ( &
speed = '''''''' ' 3nal speed
time x 1.46
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G. )&nitial speed when 'nal speed, distance traveledand deceleration are known (task 40-40)!
Example:
1. A vehicle is traveling at an unnon speed.
2. he vehicle decelerates at ".0 !eet per second per
second covering a distance o! 100.0 !eet& reaching a
3nal speed o! 50.0 miles per hour.
3. #hat as the speed o! the vehicle e!ore
deceleration$
%olution:
speed x 1.467,2 +2 x deceleration x
distance,467
H. &nitial speed when 'nal speed,distance traveled and dra# factor are known (task 40-40*!
Example:
)
+3nal speed
= ''''' '
'''''''''
miles &
50.0 ' ' x
1.467hour
!eet
2 x".0
x 100.0 !eet
miles
hour
second
speed=
=52.71.4
67
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I.A vehicle is traveling at an unnon speed.
2. he vehicle decelerates ith a drag !actor o! 0.15
covering a distance o! 100.0 !eet& reaching a 3nal
speed o! 50.0 miles per hour.
3. #hat as the speed o! the vehicle e!oredeceleration$
%olution:
speed
=
speed = 54."
I. &nitial speed when 'nal speed, deceleration
time and deceleration are known (task 40-
40+!
!eet
+3nal speed x1.467,
2
2 x drag !actor
x "2.2
467
xdistancesecon
d
(( ( miles & .
50.0 ' ' x1.467
hour
!eet
x 100.0 !eet
2 x 0.15"2.2
second
miles
hour
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Example:
1. A vehicle is traveling at an unnon speed.
2. he vehicle decelerates at ".0 !eet per second per
second !or a duration o! /.0 seconds& reaching a 3nal
speed o! 40.0 miles per hour.
3. #hat as the speed o! the vehicle e!ore
deceleration$
%olution:
deceleration x time1.467
&nitial speed when 'nal speed, deceleration time anddra# factor are known (task 40-40!
Example:
1. A vehicle is traveling at an unnon speed.
2. he vehicle decelerates ith a drag !actor o! 0.15
speed = 3nalspeed
!eetsecond2
".0
x /.0 seconds
miles
hour
miles
hour
speed=
40.0
=56.4
1.467
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!or a duration o! /.0 seconds& reaching a 3nal speed o!
"0.0 miles per hour.
3. #hat as the speed o! the vehicle e!ore
deceleration$
%olution:
!eet
drag !actor x "2.2
speed = 3nal speed
1.467
!eet
second2
1.46
xtimesecon
d
0.15 x"2.2
x /.0 seconds
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4.17 )Tasks that Yield a Vehicle.s /onstant
Velocit
1 /onstant velocit when distance traveled and time
are known (task %0-00!
Example:
1. A vehicle is traveling at an unnon velocit8.
2. he vehicle covers a distance o! 100.0 !eet in 10.0
seconds.
3.#hat is the velocit8 o! the vehicle$
%olution:
& . distance 100.0 !eet !eet
velocit8 = 9''''''''''''''' = = 10.0
time 10.0 seconds second
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4.18 Tasks that Yield 1ttained Velocit
when a Vehicle 1ccelerates from 2est
A. 1ttained velocit when distance traveled and timeare known (task %0-0!
Example:
1. A vehicle is at rest.
2. he vehicle accelerates covering a distance o! 100.0
!eet in 10.0 seconds.
3. #hat is the velocit8 o! the vehicle a!ter acceleration$
%olution:
& . 2 x distance 2 x 100.0 !eet !eet
velocit8 = '''''' = '''''''''''' = 20.0''''
time 10.0seconds second
B. 1ttained velocit when distance traveled andacceleration are known (task %0- 0"!
Example:
1. A vehicle is at rest.
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2. he vehicle accelerates at 7.0 !eet per second per
second through a distance o! 100.0 !eet.
3. #hat is the velocit8 o! the vehicle a!ter acceleration$
%olution:
velocit8 = ;2
x acceleration x distance
< !eet !eet
velocit8 ='''''''''''2 x 7.0'''''''''''''''' x 100.0
!eet = "7.4'''''''''
; second second
C. 1ttained velocit when
distance traveled and acceleration
factor are known (task %0-0$!
Example:
1. A vehicle is at rest.
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2. he vehicle accelerates ith an acceleration !actor
o! 0.1 through a distance o! 100.0 !eet.
3. #hat is the velocit8 o! the vehicle a!ter acceleration$
%olution:
!eet
velocit8 = 2 x acceleration !actor x "2.2 xdistance
second
f*6£t fppt
velocit8 = 12 x 0.1 x "2.2 x 100.0 !eet =
25.4
second second
D. 1ttained velocit whenacceleration and time are known (task %0-04!
Example:
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1. A vehicle is at rest.
2. he vehicle accelerates at 5.0 !eet per second per
second !or 10.0 seconds.
3. #hat is the velocit8 o! the vehicle a!ter acceleration$
%olution:
velocit8 = acceleration x time = 5.0''''''''''''''''''''x 10.0 seconds = 50.0''''''''''
second second
E. 1ttained velocit when acceleration factor and timeare known (task %0-0%!
Example:
1. A vehicle is at rest.
2. he vehicle accelerates ith an acceleration !actor o!
0.15 !or 10.0 seconds.
3. #hat is the velocit8 o! the vehicle a!ter acceleration$
%olution:
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velocit8 = acceleration !actor x "2.2 9)t
& x
timesecond>
fppt fpet
velocit8 = 0.15 x "2.2''''''''''''''''''''''''' x
10.0 seconds = 4/." '''''''''''''''''''''''''''
second second
4.19 Tasks that Yield &nitial Velocitwhen a Vehicle Decelerates to a Stop
A. &nitial velocit when deceleration distance and timeare known (task %0-"0!
Example:
1. A vehicle is traveling at an unnon velocit8.
2.he vehicle decelerates to a complete stop
covering a distance o! 100.0 !eet in 10.0 seconds.
3. #hat is the initial velocit8 o! the vehicle$
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%olution:
& . 2 xdistance 2 x 100.0!eet ?.. !eet
velocit8 = ''''''' = '''''''''''' = 20.0''''''
time 10.0seconds second
B. &nitial velocit when deceleration distance anddeceleration are known (task %0-
"0"!
Example:
1. A vehicle is traveling at an unnon velocit8.
2. he vehicle decelerates to a complete stop at 7.0
!eet per second per second through a distance o! 100.0
!eet.
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velocit8 = ';2 x deceleration x distance
feet feet
velocit8 = 12 x 7.0 =' x 100.0 !eet = "7.4
second second
C. &nitial velocit when deceleration distance and dra#factor are known (task %0-
"0$!
Example:
1. A vehicle is traveling at an unnon velocit8.
2. he vehicle decelerates to a complete stop ith a
drag !actor o! 0.1 !or a distance o!
3. #hat is initial the
velocit8 o! the vehicle$
%olution:
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100.0!eet.
3. #hat is the initial velocit8 o! the vehicle$
%olution:
!eet
velocit8 = @2 x drag !actor x "2.2 x distancesecond2
feet feet
velocit8 = 12 x 0.1 x "2.2 x 100.0 !eet = 25.4
second second
D. &nitial velocit when deceleration and decelerationtime are known (task %0-"04!
Example:
1. A vehicle is traveling at an unnon velocit8.
2. he vehicle decelerates to a complete stop at 5.0
!eet per second per second !or 10.0 seconds.
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3. #hat is the initial velocit8 o! the vehicle$
%olution:
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velocit8 = deceleration x time = 5.0 x 10.0 seconds =50.0
E. &nitial velocit whendra# factor anddeceleration time are known (task %0-"0%!
Example:
1. A vehicle traveling at an unnon velocit8.
2. he vehicle decelerates to a complete stop ith a
drag !actor o! 0.15 !or 10.0 seconds.
3. #hat is the initial velocit8 o! the vehicle$
%olution:
velocit8 = drag !actor x "2.2 9 0 xtime
@ second2
fppt fppt
velocit8 = 0.15 x "2.2 9x 10.0 seconds = 4/."second second
x 10.0 seconds =50.0
B' second second
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4.20 Tasks that Yield Velocit when a
Vehicle 1ccelerates from One Velocit toa Faster Velocit
A. Final velocit when initial velocit, distancetraveled and acceleration time are known (task %0-$0!
Example:
1. A vehicle is traveling at 55.0 !eet per second.
2. he vehicle accelerates covering a distance o! 1/0.0
!eet in ".0 seconds.
3. #hat is the velocit8 o! the vehicle a!ter acceleration$
%olution:
& . 2 x distance . . . . & .
velocit8 = '''''' ' initial velocit8
time
. . 2 x 1/0.0 !eet ) !eet ' !eet
velocit8 =''''''''''' 55.0 ''' = 65.0 '''
B. seconds second secondFinal velocit when
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initial velocit, distance traveled and acceleration are
known (task %0-$0"!
Example:
1. A vehicle is traveling at 55.0 !eet per second.
2. he vehicle accelerates at ".0 !eet per second per
second covering a distance o! 100.0 !eet.
3. #hat is the velocit8 o! the vehicle a!ter acceleration$
%olution:
velocit8 = )*+initial velocit8,1 +2 x acceleration x
distance,
1 x acceleration !actor x "2.2
second
velocit8 =
!eetsecond
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C. Final velocit when initial velocit, distance
traveled and acceleration factor are known (task %0-$0$!
Example:
1. A vehicle is traveling at 55.0 !eet per second.
2. he vehicle accelerates ith an acceleration !actor
o! 0.15 covering a distance o! 100.0 !eet.
3. #hat is the velocit8 o! the vehicle a!ter acceleration$
%olution:
!eet
seco
nd
velocit8 = velocit8 = 6".2
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D. Final velocit when initial velocit, accelerationtime and acceleration are known (task %0-$04!
Example:
1. A vehicle is traveling at 55.0 !eet per second.
2. he vehicle accelerates at ".0 !eet per second persecond !or a duration o! /.0 seconds.
3. #hat is the velocit8 o! the vehicle a!ter acceleration$
%olution:
velocit8 = initial velocit8 +acceleration x time,
E. Final velocit when 'nal velocit, accelerationtime and acceleration factor are known (task %0-$0%!
Example:
1. A vehicle is traveling at 55.0 !eet per second.
2. he vehicle accelerates ith an acceleration !actor
o! 0.15 !or a duration o! /.0 seconds.
!eetsecond2
!eet
second
!eet
second
velocit8=
".0
x /.0 seconds
=7C.0
55.0
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3. #hat is the velocit8 o! the vehicle a!ter acceleration$
%olution
:
feet feet feet
velocit8 = 55.0 0.15 x "2.2 ' x /.0 seconds = C".6
second@ 6 second @ secon
!eetsecond2
acceleration !actorx "2.2
xtime
velocit8 = initialvelocit8
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F. d&nitial velocit when 'nal velocit, distancetraveled and acceleration time are known (task %0-$0!
Example:
1. A vehicle is traveling at an unnon velocit8.
2. he vehicle accelerates covering a distance o!
400.0 !eet in 6.0 seconds& reaching a 3nal velocit8 o!
75.0 !eet per second.
3. #hat as the velocit8 o! the vehicle e!ore
acceleration$
%olution:
. . 2 xdistance .
velocit8 = ''''''' ' 3nal velocit8
time
2 x 400.0 !eet !eet co !eet
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velocit8 =''''''''''' 75.0 ''' = 5/." ' '
6.0 seconds secondsecond
G. &nitial velocit when 'nal velocit, distancetraveled and acceleration are known (task %0-$0)!
Example:
1. A vehicle is traveling at an unnon velocit8.
2. he vehicle accelerates at ".0 !eet per second per
second covering a distance o! 100.0 !eet& reaching a
3nal velocit8 o! 60.0 !eet per second.
3. #hat as the velocit8 o! the vehicle e!ore
acceleration$
%olution:
velocit8 = 'B&*+3nal velocit8,2 ' +2 x acceleration x
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distance,
H. &nitial velocit when 'nal velocit, distancetraveled and acceleration factor are known (task %0-$0*!
Example:
I.A vehicle is traveling at an unnon velocit8
2. he vehicle accelerates ith an acceleration !actor
o! 0.15 covering a distance o! 100.0 !eet& reaching a
3nal velocit8 o! 65.0 !eet per second.
3. #hat as the velocit8 o! the vehicle e!ore
acceleration$%olution:
velocit8 = ...
...)+3nalvelocit8,
2
!eet
2 x acceleration !actor x "2.2 r' xdistance
secon
d
!eetsecond2
!eet
second
x 100.0 !eet
=54./
velocit8 =
2 x".0
!eet
second
x 100.0 !eet
velocit8=
65.0
2 x 0.15"2.2 secon
d
!eet
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velocit8 = 57.1
& &nitial velocit when 'nal velocit, acceleration timeand acceleration are known (task %0-$0+!
Example:
1. A vehicle is traveling at an unnon velocit8.
2. he vehicle accelerates at ".0 !eet per second per
second !or a duration o! /.0 seconds& reaching a 3nal
velocit8 o! /0.0 !eet per second.
3. #hat is the velocit8 o! the vehicle a!teracceleration$
%olution:
velocit8 = 3nal velocit8 ' +acceleration x time
,
!eet
second
!eet
second
!eet
second
!eet
second2
=56.0
velocit8=
".0
x /.0 seconds
/0.0
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&nitial velocit when 'nal velocit, accelerationtime and acceleration factor are known (task %0-$0!
Example:
1. A vehicle is traveling at an unnon velocit8.
2. he vehicle accelerates ith an acceleration !actor
o! 0.15 !or a duration o! /.0 seconds& reaching a 3nal
velocit8 o! C0.0 !eet per second.
3. #hat as the velocit8 o! the vehicle e!ore
acceleration$
%olution:
acceleration !actor x "2.2 9)eet
2 x time
second4.21 Tasks that Yield Velocit when a
Vehicle Decelerates from One Velocit to aSlower Velocit
A. Final velocit when initial velocit, distancetraveled and deceleration time are known (task %0-
velocit8 = 3nalvelocit8
C0.0!eeD = 51.4
!cetvelocit8= secon
d
secon
d
feet
0.15 x "2.2'''r' x /.0
secondssecond
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40!
Example:
1. A vehicle is traveling at 50.0 !eet per second.
2. he vehicle decelerates covering a distance o!
200.0 !eet in 5.0 seconds.
3. #hat is the velocit8 o! the vehicle a!ter
deceleration$
%olution:
& . 2 x distance . . . . & .
velocit8 = ''''''' ' initial velocit8
time
& . 2x 200.0 !eet (( ( !eet .. ( !eet
velocit8 =''''''''''' 50.0 ''' = "0.0
seconds second secon
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d
5.0
B. Final velocit when initial velocit, distancetraveled and deceleration are known (task %0-40"!
Example:
1. A vehicle is traveling at 55.0 !eet per second.
2. he vehicle decelerates at ".0 !eet per second per
second covering a distance o! 100.0 !eet.
3.#hat is the velocit8 o! the vehicle a!ter
deceleration$
%olution:
velocit8 = ')*+initial velocit8,2 ' +2 x deceleration x
distance,
C. Final velocit when initial velocit, distancetraveled and dra# factor are known (task %0-40$!
Example:
!eet
second
!eetsec
ond2
!eet
second
velocit8=
55.0
2 x".0
x 100.0 !eet
=4C.2
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1. A vehicle is traveling at 55.0 !eet per second.
2. he vehicle decelerates ith a drag !actor o! 0.15
covering a distance o! 100.0 !eet.
3. #hat is the velocit8 o! the vehicle a!ter
deceleration$
%olution
:
velocit8 = 45.
D. 4Final velocit when initial velocit, decelerationtime and deceleration are known (task %0-404!
Example:
1. A vehicle is traveling at 55.0 !eet per second.
2. he vehicle decelerates at ".0 !eet per second per
!eet
... *+initialvelocit8,
2 '2 x drag !actor x"2.2
xdistancesecon
d>
!eet
second
!eetvelocit8=
55.0
2 x 0.15"2.2
x 100.0 !eetsecon
d
!eet
second
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second !or a duration o! /.0 seconds.
3. #hat is the velocit8 o! the vehicle a!ter
deceleration$
%olution:
velocit8 = initial velocit8 ' +deceleration x time,
E. Final velocit when initial velocit, decelerationtime and dra# factor are known (task %0-40%!
Example:
1. A vehicle is traveling at 55.0 !eet per second.
2. he vehicle decelerates ith a drag !actor o! 0.15
!or a duration o! /.0 seconds.
3. #hat is the velocit8 o! the vehicle a!ter
deceleration$
%olution
:
!eet
second
!eet
!eet
second
velocit8=
55.0
".0
x /.0 seconds
="1.0secon
d
!eet
drag !actor x"2.2
xtimesecon
d
velocit8 = initialvelocit8
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F. &nitial velocit when 'nal velocit, distancetraveled and deceleration time are known (task %0-40!
Example:
1. A vehicle is traveling at an unnon velocit8.
he vehicle decelerates covering a distance o! 200.0
!eet in 5.0 seconds& reaching a 3nal velocit8 o! "0.0
!eet per second
.
2.
& . 2 xdistance ( & & .
velocit8 = ''''''' ' rinal velocit8
time
!eet
second
!eetsecond2
!eet
second
velocit8=
55.0
x /.0 seconds
0.15 x"2.2
=16.4'
3. #hat as the velocit8 o! thevehicle e!ore deceleration$ %olution:
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& . 2 x 200.0 !eet ( !eet !eet
velocit8 ''''''''''''''''''''''' "0.0 ''''' = 50.0'''''''
5.0 seconds secondsecond
G. Final velocit when initial velocit, distancetraveled and deceleration are known (task %0-40)!
Example:
1. A vehicle is traveling at an unnon velocit8.
2. he vehicle decelerates at ".0 !eet per second per
second covering a distance o! 100.0 !eet& reaching a
3nal velocit8 o! 50.0 !eet per second.
3. #hat as the velocit8 o! the vehicle e!ore
deceleration$
%olution:
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velocit8 = )*+3nal velocit8,2 +2 x deceleration x
distance,
H. &nitial velocit when 'nal velocit, distancetraveled and dra# factor are known (task %0-40*!
Example:
I.A vehicle is traveling at an unnon velocit8.
2. he vehicle decelerates ith a drag !actor o! 0.15
covering a distance o! 100.0 !eet& reaching a 3nal
velocit8 o! 45.0 !eet per second.
3. #hat as the velocit8 o! the vehicle e!ore
deceleration$
%olution
!eet
second
!eetsecond2
!eet
second
x 100.0 !eet
=55.7
velocit8=
50.0
2 x".0
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:!eet
2 x drag !actor x"2.2second
&
)
?
! e
e
t
+3nalvelocit8,
2
xdistance
velocit8 =
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v
e
l
o
c
i
t
8
=
5
4
.
7
second
& &nitial velocitwhen 'nal velocit,deceleration time
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and deceleration are known (task %0-40+!
Example:
1. A vehicle is
traveling at anunnon velocit8.
2. he vehicle
decelerates at ".0
!eet per second per
second !or a
duration o! /.0
seconds& reaching a
3nal velocit8 o!
"0.0 !eet per
second.
3. #hat as the
velocit8 o! the vehicle
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e!ore deceleration$
%olution:
velocit8 = 3nal
velocit8
+deceleration x time, &nitial velocitwhen 'nal velocit,deceleration timeand dra# factor are known (task %0-40!
Example:
1. A vehicle is
traveling at an
unnon velocit8.
2. he vehicle
decelerates ith a
drag !actor o! 0.15
!or a duration o!
!eet
secon
d
!eet
velocit8=
"0.0
".0
x /.0 seconds
second
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/.0 seconds& reach'
ing a 3nal velocit8
o! 20.0 !eet per
second.
3. #hat as thevelocit8 o! the vehicle
e!ore deceleration$
%olution
:!eet
drag !actor x "2.2 r'x time
second
4.22 Tasks that Yield 1ccelerationwhen a Vehicle1ccelerates from
2est A. 1ccelerationwhen accelerationdistance and time are known (task 0-0!
velocit8 = 3nalvelocit8
!eet
second
!eetsecond2
velocit8=
x /.0 secon
20.0
0.15 x"2.2
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Example:
1. A vehicle is at
rest.
2. he vehicle
accelerates covering a
distance o! "0.0 !eet
in ".0 seconds.
3. #hat is the
acceleration o! thevehicle$
%olution:
& 2 xdistance
2 x"0.0!eet
( !eet
acceleration =''''''''''''''''''
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5
'''''''''''''''''' ='''''''''''''''''' = 6.7''''''''''''''''''r
ti
me
+".0
seconds,
second
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B. 1ccelerationwhen attained speedand time are known(task 0-0"!
Example:
1. A vehicle is at
rest.
2. he vehicle
accelerates to a speed
o! "0.0 miles per
hour.
3. he duration o!
the acceleration is 5.0
seconds.
4. #hat is the
acceleration o! the
vehicle$
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%olution:
miles
acceleration 3
%%66i)6 3 $00
4)
//
(@ee)
time 5.0
seconds
second
C. 1ccelerationwhen attained speedand distance are known (task 0-0$!
Example:
A vehicle is at rest
.
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1.
2. he vehicle
accelerates to a
speed o! "5.0 miles
per hour through a
distance o! 150.0
!eet.
3. #hat is the
acceleration o! the
vehicle$
%olution:
D. 1ccelerationwhen attained velocit and time are known (task 0-04!
Example:
1. A vehicle is at
2 x 150.0!eet
acceleration =
+speed x1.467,
2 2
x distance
.. ( miles & .
"5.0 ' ' 1.467
hour
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rest.
2. he vehicle
accelerates to a
velocit8 o! "0.0 !eet
per second.
3. he duration o!
the acceleration is 5.0
seconds.
4. #hat is theacceleration o! the
vehicle$
%olution:
"0.0'F
)acceleration3
seco5d 3 6
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time 5.0 seconds
second
E. 1cceleration
when attained velocit and distanceare known (task 0-0%!
Example:
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1. A vehicle is at
rest.
2. he vehicle
accelerates to a
velocit8 o! "5.0 !eetper second in a
distance o! 150.0 !eet.
3. #hat is the
acceleration o! the
vehicle$
%olution
:!eet
second
"5.0
velocit82
2 xdistance
acceleration =
=42 x 150.0
!eetsd
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4.23 Tasks that Yield 1cceleration when a Vehicle 1ccelerates from One Speed or Velocit to a Faster Speed or Velocit
A. 1cceleration when initial speed, 'nal speed andtime are known (task 0-"0!
Example:
1. A vehicle is traveling at a speed o! 40.0 miles per
hour.
2. he vehicle accelerates to a speed o! 50.0 miles per
hour in 2.0 seconds.
3. #hat is the acceleration o! the vehicle$
%olution:
+3nal speed x 1.467, ' +initial speed x1.467,
acceleration = '''''''''''''''''''''''''''''''''time
B. 1cceleration when initial speed, 'nal speed anddistance are known (task 0-"0"!
!eetsecond2
=7."
acceleration =
2.0 seconds
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Example:
1. A vehicle is traveling at a speed o! 40.0 miles perhour.
2. he vehicle accelerates to a speed o! 50.0 miles perhour in a distance o! 100.0 !eet.
3. #hat is the acceleration o! the vehicle$
%olution:
+3nal speed x 1.467,2 ' +initial speed x
1.467,2
acceleration =E'''''''''''''''''''''
H ''''''''''''
2 x distanc
e
C. 1cceleration when initial velocit, 'nal velocit andtime are known (task 0-$0!
Example:
1. A vehicle is traveling at a velocit8 o! 40.0 !eet per
second.
2. he vehicle accelerates to a velocit8 o! 50.0 !eet per
second in 2.0 seconds.
I40.0 )
hour
mile
shour
x
1.467
x
1.467
50.
0
!eet
second2
=C.7acceleration = 2 x 100.0 !eet
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3. #hat is the acceleration o! the vehicle$
%olution:
+3nal velocit8, ' +initial velocit8,time
D. 1cceleration when initial velocit, 'nal velocit anddistance are known (0-$0"!
Example:
1. A vehicle is traveling at a velocit8 o! 40.0 !eet per
second.
2. he vehicle accelerates to a velocit8 o! 50.0 !eet per
second in a distance o! 100.0 !eet.
3. #hat is the acceleration o! the vehicle$
%olution:
+3nal velocit8,2 ' +initial velocit8,
2
acceleration = ''''''''''''''''''''' 9
acceleration = !eet
second
!eet
second
50.
0
40.
0
!ee
tacceleration =
=5.02.0
secondssecond
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2 x distanc
e!eet
second
50.0
40.0
!eetsecond2
acceleration
=4.52 x 100.0
!eet
!eet
second
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4.24 Tasks that Yield 1cceleration Factor
when a Vehicle 1ccelerates from 2est A. 1cceleration factor when acceleration distance andtime are known (task )0-0!
Example:
1. A vehicle is at rest.
2. he vehicle accelerates covering a distance o! "0.0
!eet in ".0 seconds.
3. #hat is the acceleration !actor o! the vehicle$
%olution:
2 x
distance acceleration
!actor = ''''''''''''''''''
2 ((( !eet
time x "2.2"
second
acceleration !actor = 2 x "0.0 !eet999( )
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2 ) !eet
+".0 seconds, x "2.2
second
B. 1cceleration factor when attained speed and timeare known (task )0-0"!
Example:
1. A vehicle is at rest.
2. he vehicle accelerates to a speed o! "0.0 miles per
hour.
3. he duration o! the acceleration is 5.0 seconds.
4. #hat is the acceleration !actor o! the vehicle$
%olution:
miles & t*r (
sneed x 1 467 "0.09 x 1.467
acceleration !actor = ' ' '''''''''''''''')9'9 = '''''''''''''''''''''''''''9'9 =0."time x "2.29997 5.0 seconds x "2.29
second> second
C. 1cceleration factor when attained speed anddistance are known (task )0-0$!
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Example:
1. A vehicle is at rest.
2. he vehicle accelerates to a speed o! "5.0 miles per
hour in a distance o! 150.0 !eet.
3. #hat is the acceleration !actor o! the vehicle$
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%olution:. . .+speed x1.467,
acceleration !actor = ''''''''''
? ? !eet
2 x distance x "2.2second2
second
D. 1cceleration factor whenattained velocit and time are known (task )0-04!
Example:
1. A vehicle is at rest.
2. he vehicle accelerates to a
velocit8 o! "0.0 !eet per second.
3. he duration o! the
acceleration is 5.0 seconds.
acceleration!actor =
=0."
eet
. ( ( miles & &
"5.0 ' ' x1.467
hour
2 x 150.0 !eet x"2.2
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4. #hat is the acceleration !actor
o! the vehicle$
%olution:
30.
0!eet
acceleration !actor = ''''''''''''''''''''''''velocit8 9(9 ( '''''''''''''''''''''''''second9(9(9 ( J 2
time x "2.2 966 ?5.0
secondsx "2.2
66
second2
second)
E. 1cceleration factor whenattained velocit and distance are known (task )0-0%!
Example:
1. A vehicle is at rest.
2. he vehicle accelerates to a
velocit8 o! "5.0 !eet per second in
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a distance o! 150.0 !eet.
3. #hat is the acceleration !actor
o! the vehicle$
%olution:
ve
locit82
acceleration !actor =
? ...
!eet
2 x
distance
x "2.2
secon
d
acceleration!actor =
= 0.1
2 x 150.0 !eetx "2.2
!eetsecond2
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4.25 Tasks that Yield1cceleration Factor when a Vehicle 1ccelerates fromOne Speed or Velocit to a Faster Speed or Velocit
A. 1cceleration factor wheninitial speed, 'nal speed andtime are known (task )0- "0!
Example:
1. A vehicle is traveling at a
speed o! 40.0 miles per hour.
2. he vehicle accelerates to a
speed o! 50.0 miles per hour in
2.0 seconds.
3. #hat is the acceleration !actor
o! the vehicle$
%olution:
+3nal speed x1.467, '+initial speedx 1.467,
acceleration !actor = ''''''''H
''''''''''''''''''''''''''''''''''7
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9''''''''''''''''''
!eet
time x"2.2''''''''r'
second
B. 1cceleration factor wheninitial speed, 'nal speed anddistance are known (task )0-"0"!
Example:
1. A vehicle is traveling at a
speed o! 40.0 miles per hour.
2. he vehicle accelerates to a
speed o! 50.0 miles per hour
through a distance o! 100.0 !eet.
3. #hat is the acceleration !actor
o! the vehicle$
= 0
acceleration!actor = +2.0 seconds, x
"2.2
fe
etsecond
2
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%olution
:+3nal speed x 1.467,
2 ' +initial
speed x 1.467,
acceleration !actor =
! ee
t
2 x distance x"2.2
C. 1cceleration factor wheninitial velocit, 'nal velocit andtime are known (task )0-$0!
Example:
1. A vehicle is traveling at a
velocit8 o! 40.0 !eet per second.
2. he vehicle accelerates to a
velocit8 o! 50.0 !eet per second in
2.0 seconds.
acceleration!actor =
=0."2 x 100.0 !eet x "2.2
!eet second2
second
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3. #hat is the acceleration !actor
o! the vehicle$
%olution:
+3nal velocit8, '+initial velocit8,
!eet
time x"2.2
second
seco
ndD. 1cceleration factor wheninitial velocit, 'nal velocitand distance are known (task)0-$0"!
Example:
1. A vehicle is traveling at a
velocit8 o! 40.0 !eet per second.
2. he vehicle accelerates to a
velocit8 o! 50.0 !eet per second in
acceleration!actor =
!eet
second
!eet
second
50.0
40.0
= 0.2
!eet
2.0 seconds x"2.2
acceleration!actor =
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a distance o! 100.0 !eet.
3. #hat is the acceleration !actor
o! the vehicle$
%olution:
+3nal
velocit8,2 '+initialvelocit8,
2
acceleration !actor = '''''''''''''''''''''''''''''''7979'9
. ?
?!eet
2 xdistancex "2.2'''''''''''
second!eet
second
!eet
second
50.0
40.0acceleration
!actor = 9
= 0.1
!eetsecond2
2 x 100.0 !eet x"2.2
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4.26 Tasks that Yield Deceleration when a Vehicle Decelerates to a Stop
A. Deceleration when deceleration distance and time
are known (task *0-0!
Example:
1. A vehicle is traveling at a constant speed.
2. he vehicle decelerates to a complete stop
covering a distance o! "0.0 !eet in ".0 seconds.
3. #hat is the deceleration o! the vehicle$
%olution:
2 x distance 2 x "0.0 !eet & ( !eet
deceleration = ' ''' = '''''''''' = 6.7''''
time +".0seconds, second
B. Deceleration when initial speed and decelerationtime are known (task *0-0"!
Example:
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1. A vehicle is traveling at a speed o! "0.0 miles per
hour.
2. he vehicle decelerates to a complete stop.
3. he duration o! the deceleration is 5.0 seconds.
4. #hat is the deceleration o! the vehicle$
%olution:
miles
. speed x 1.467 > hour
o o ! eet
deceleration = 9'' = '''' ' ''''''''''''''''''''' =
/./ ''''''''''''''''''''
time 5.0seconds second
Deceleration when initial speed and distance are known
(task *0-0$!
x1.467
"5.0
!eet
= 8.8
2 x 150.0!eet
second
Example:
1. A vehicle is traveling at a speed o! "5.0 milesper hour.
2. he vehicle decelerates to a complete stopthrough a distance o! 150.0 !eet.
3. #hat is the deceleration o! the vehicle$
%olution:
miles
^ II
+speed x 1.467,2
deceleration = 2 x
distance
hour
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C. Deceleration when initial velocit and timeare known (task *0-04!
Example:
1. A vehicle is traveling at a velocit8 o! "0.0
!eet per second.
2. he vehicle decelerates to a complete stop.
3. he duration o! the deceleration is 5.0
seconds.
4. #hat is the deceleration o! the vehicle$
%olution:
"0.0
deceleration = ''''''second = 6 0 (@eet
time 5.0 seconds second
D. Deceleration when initial velocit anddistance are known (task *0-0%!
Example:
1. A vehicle is traveling at a velocit8 o! "5.0
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!eet per second.
2. he vehicle decelerates to a complete stop
through a distance o! 150.0 !eet.
3. #hat is the deceleration o! the vehicle$
%olution:
4.27 Tasks that Yield Decelerationwhen a Vehicle Decelerates from oneSpeed or Velocit to a Slower Speed or Velocit
1 Deceleration when initial speed, 'nal speedand time are known (task *0-"0!
Example:
1. A vehicle is traveling at a speed o! 50.0 miles
per hour.
2. he vehicle decelerates to a speed o! 40.0
miles per hour in 2.0 seconds.
3. #hat is the deceleration o! the vehicle$
!eetsecond
"5.0 !eetsecond2
deceleration =
=4.12 x 150.0
!eet
velocit8
2 2 x
distance
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%olution:
A((&((((((( +initial speed x 1.467, ' +3nalspeed x 1.467,
deceleration 9 ''''''''''''''''''''''''''''''
tim
e
C.Deceleration when initial velocit, 'nal
velocit and time are known (task *0-$0!
) ? miles &
40.0 ' ' x1.467
hour
? ) miles & .
50.0 ' ' x1.467
hour
!eet=7."
deceleration = 2.0 seconds second2
6 Deceleration when initial speed, 'nal speed and distance
are known (task *0-"0"!
Example:
1. A vehicle is traveling at a speed o! 50.0 miles per hour.
2. he vehicle decelerates to a speed o! 40.0 miles per
hour through a distance o! 100.0 !eet.
3. #hat is the deceleration o! the vehicle$
%olution:
+initial speed x 1.467,2 ' +3nal
speed x 1.467,2 2 x distance
deceleration
2 x 100.0 !eet second
2!eet
=C.7
deceleration =
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Example:
1. A vehicle is traveling at a velocit8 o! 50.0
!eet per second.
2. he vehicle decelerates to a velocit8 o! 40.0
!eet per second in 2.0 seconds.
3. #hat is the deceleration o! the vehicle$
%olution:
+initial velocit8, ' +3nal velocit8,
tim
e
deceleration =
!eet
second
!eet
second
50.0
40.0
!eet
deceleration
=5.02.0
secondssecond
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D. Deceleration when initial velocit, 'nal velocit
and distance are known (task *0- $0"!
Example:
1. A vehicle is traveling at a velocit8 o! 50.0 !eet per
second.
2. he vehicle decelerates to a velocit8 o! 40.0 !eet per
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second in a distance o! 100.0 !eet.
3. #hat is the deceleration o! the vehicle$
%olution:
+initial velocit8,2 ' +3nal velocit8,
2 2 x
distancedeceleration =
!eet
second
!eet
second
50.0
40.0 !eetdeceleratio
n ==4.52 x 100.0
!eetsecond
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Glossary
1cceleration
he mathematical opposite o! deceleration. Acceleration
is the rate o! change o! an oectKs speed or velocit8
ith respect to time ith speed or velocit8 ecoming
greater over time. <n this text& acceleration ill e
presented ith units o! !eet per second per second.
1cceleration Factor
A percentage or !raction o! the earthKs gravit8 constant
+"2.2 !eet per second per second, used to descrie the
magnitude o! an acceleration or deceleration.
Acceleration !actor is descried in g num4ers such that a
!ractional g'value is eJual to the eJuivalent !raction o!
the earthKs gravit8 constant. Lor example& 0.5 g is
exactl8 eJual to "2.2 !eet per second per second
multiplied 8 0.5& or 16.1 !eet per second per second.
+%ee Mrag Lactor,.
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6rakin# Distance
he distance reJuired !or a vehicle to come to a
complete stop !rom the point at hich the actual raing
process egins.
/oe7cient of Friction (/OF!
he ratio o! lateral !orce reJuired to move one oectacross another oect to the eight o! the oect eingmoved. Lor example& i! it reJuires a !orce o! 5.0 poundsto push a 10.0' pound ox across a tale top& then thecoeNcient o! !riction eteen the ox and the tale topis the result o! dividing the lateral !orce +5.0 pounds, 8the eight o! the ox +10.0 pounds,. his 8ields acoeNcient o! !riction o! 0.5. <n realit8& the coeNcient o! !riction eteen to sur!aces has to values. One value
is that hich is evident prior to movement& hich iscalled the static coeNcient o! !riction +%OL,. he othervalue is that hich is evident during movement& hich iscalled the d8namic coeNcient o! !riction +MOL,. <ngeneral& the static coeNcient o! !riction is greater thanthe d8namic coeNcient o! !riction. <n this text& the termcoeNcient o! !riction +OL, ill re!er to the d8namiccoeNcient o! !riction.
/onstant
A mathematical Juantit8 or value that does not change.
/onversion Factor
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A constant 8 hich a value is multiplied or divided to
8ield an eJual value ith a diPerent unit o! measure.
Deceleration
he mathematical opposite o! acceleration. Meceleration is
the rate o! change o! an oectKs speed or velocit8 ithrespect to time ith speed or velocit8 ecoming less over
time. <n this text& deceleration ill e presented ith units
o! !eet per second per second.
Densit
he ratio o! an oectKs eight to its volume. Lor
example& i! a loc o! ice is exactl8 one !oot in height&
idth and length its volume is exactl8 one cuic !oot. One
cuic !oot o! ice eighs aout 62.0 pounds. here!ore& the
densit8 o! ice is approximatel8 62.0 pounds per cuic
!oot. Alternativel8& a cuic !oot o! steel eighs aout
4C0.0 pounds and& there!ore& has a densit8 o! 4C0.0
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pounds per cuic !oot. Qecause o! these values& it is clear
that the densit8 o! steel is almost eight times that o! ice.
Dra# Factor
A percentage or !raction o! the earthKs gravit8 constant
+"2.2 !eet per second per second, used to descrie themagnitude o! an acceleration or deceleration. Mrag !actor
is descried in g num4ers such that a !ractional g'value is
eJual to the eJuivalent !raction o! the earthKs gravit8
constant. Lor example& 0.5 g is exactl8 eJual to "2.2 !eet
per second per second multiplied 8 0.5& or 16.1 !eet per
second per second. +%ee Acceleration Lactor,.
Friction
he resistance to motion that arises hen one oect ismoved across another. Lriction is that !orce hich actseteen an oect and the sur!ace across hich the oect
is eing moved to resist the sliding motion eteen theto oects.
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8ravit /onstant (#!
he acceleration o! oects resulting !rom the ePect o!
earthKs gravit8 upon the oect. Rear the earthKs sur!ace&
this acceleration is approximatel8 "2.2 !eet per second per
second. <n this text& as in most others& the areviation !or
earthKs gravit8 constant ill e g.
9erception:2eaction Distance
he distance through hich a vehicle travels hile thedriver is processing in!ormation that ill give rise to a
decision regarding a response to a given stimulus or set o! stimuli.!eet