AP Physics B - Kinematics

7/18/2019 AP Physics B - Kinematics

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Kinematics

AP Physics B



Defning the important

variables

Kinematics is a way of describing the motion of objects

without describing the causes. You can describe anobject’s motion:

In words Mathematically Pictorially GraphicallyNo matter HOW we describe the motion, there are several KEY VARAB!E"

that we #se$

Symbol ariable !nitst %ime s

a Acceleration m&s&s

' or y (is)lacement m

vo nitial velocity m&sv *inal velocity m&s

+ or a+ Acceleration d#e to+ravity

m&s&s



The 3 Kinematic equations

%here are ma-or

.inematic e/#ations

than can be #sed to

describe the motion in"#$%I&. All are #sed

when the acceleration

is CONSTANT. )(2

2

1

22

2

oo

oo

o

x xavv

at t v x x

at vv

−+=

++=

+=



Kinematic #1

at vv

at vvt vv

t va

o

oo

+=

=−−→∆

∆=



Kinematic #1E'am)le0 % boat mo'es slowly out of a marina (so as to not

lea'e a wa)e* with a speed of +.,- ms. %s soon as itpasses the brea)water/ lea'ing the marina/ it throttles up

and accelerates at 0.1- mss$

2hat do I)now3

2hat do Iwant3

vo1 2$34 m&s v 1 5

a 1 6$74 m&s&s

t 1 3 s

a8 How 9ast is the boat movin+ a9ter acceleratin+ 9or 3 seconds5

=

+=

+=

v

v

at vv o

)5)(40.2()50.1(

+4., ms



Kinematic #2

221 at t v x x oxo ++=

b* 5ow far did the boat tra'el during that time3

=

++=

++=

x

x

at t v x x oxo

)5)(40.2(

2

1)5)(5.1(0

21

2

2

46., m



Does all this make sense?

m A

Abh A

50.7

)5.1)(5(

=

=→=

m A

bh A

30

)12)(5(2

1

2

1

=

→=

+.,

ms

+4., ms

m A

Abh A

50.7

)5.1)(5(

=

=→=

$otal displacement 7 6.,- 8 4- 7 46., m 7 $otal %9#% under the line.



Interesting to Note

vt t v x x

att t v x x

at t v x x

oxo

oxo

oxo

∆++=

++=

++=

21

21

21 2

A 1 HB

A12&6HB

:ost o9 the time, 'o14, b#t i9 it is not

don;t 9or+et to A(( in the initial

)osition o9 the ob-ect$



Kinematic #3)(222

oo x xavv −+=

2hat do I)now3

2hat do Iwant3

vo1 26 m&s ' 1 5

a 1 <$3 m&s&s

V 1 4 m&s

E'am)le0 You are dri'ing through town at +0 ms when suddenly a ball rolls

out in front of your car. You apply the bra)es and begin decelerating at

4., mss.

5ow far do you tra'el before coming to a complete stop3

=

−=−

−−+=

−+=

x x

x

x xavv oo

7144

)0)(5.3(2120

)(2

2

22

0-.,6 m



ommon !roblems "tuents$aveI don’t )now which euation to choose;;;

#uation Missing ariable

'

v

t

at vvo +=

2

2


)(222

oo x xavv −+=



Kinematics %or the &'(TI)*Direction All .inematics can be #sed to analy=e one

dimensional motion in either the > direction OR they direction$

)(2)(2

21

21

2222

22

ooy yoox

oyooxo

oy yo

y y g vv x xavv

gt t v y yat t v x x

gt vvat vv

−+=→−+=

++=→++=

+=→+=



+g, or ag - The )cceleration ue

to gravit.%he acceleration d#e to +ravity is a s)ecial constant that e'ists

in a VA?@@:, meanin+ witho#t air resistance$ 9 an ob-ect isin *REE *A!!, +ravity will <5%=G# an ob-ects velocity by $m&s every second$

2/8.9 sma g g −==

%he acceleration d#e to +ravity0C A!WAY" A?%" (OWNWAR(C" A!WAY" ?ON"%AN% near the

s#r9ace o9 Earth



'/amples% stone is dropped at rest from the top of a cliff. It is

obser'ed to hit the ground ,.6> s later. 5ow highis the cliff3

2hat do I)now3

2hat do Iwant3

voy1 4 m&s y 1 5

+ 1 <$ m&s6

yo14 m

t 1 3$D s

2hich 'ariable is =?$ gi'en and

=?$ as)ed for3

@inal elocity;

2

21 gt t v y y oyo ++=

=

−=

y

y 2)78.5(9.4)78.5)(0(

A+B4.6 m

5 7+B4.6m



'/amples% pitcher throws a fastball with a 'elocity of 14., ms. It is

determined that during the windup and deli'ery the ball co'ers adisplacement of 0., meters. $his is from the point behind thebody when the ball is at rest to the point of release. <alculate theacceleration during his throwing motion.

2hat do I)now3

2hat do Iwant3

vo1 4 m&s a 1 5

' 1 6$3 m

v 1 7$3 m&s


=?$ as)ed for3

$IM#

)(222

oo x xavv −+=

=

−+=

a

a )05.2(205.43 22

46>., mss



'/amples5ow long does it ta)e a car at rest to cross a 4,.- m

intersection after the light turns green/ if the accelerationof the car is a constant 0.-- mss3

2hat do I)now3

2hat do Iwant3

vo1 4 m&s t 1 5

' 1 3 m

a 1 6$44 m&s&s


=?$ as)ed for3

@inal elocity

=

++=

t

t 2)2(

2

1)0(035

2


,.C0 s



'/amples% car accelerates from +0., ms to 0, ms in B.-

seconds. 2hat was the acceleration3

2hat do I)now3

2hat do Iwant3

vo1 26$3 m&s a 1 5

v 1 63 m&s

t 1 s


=?$ as)ed for3

"ISP&%<#M#=$

at vvo +=

=

+=

a

a )6(5.1225

0.-> mss

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AP Physics B - Kinematics

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