Graphical Analysis of motion in _________________

I. Distance and displacement.

What is the total distance moved?What is the resultant displacement?

20 + 10 = 30 m

+10 m

d (m)

t (s)

20

10

5 10 15

one direction

Find the average speed in the 0-5 s interval.

Repeat for 5-10 s and 10-15 s.

20 m5 s

0 m ,5 s

10 m5 s

II. Uniform motion – ____________ is constant

d

t

slope =_____

A

B

= ________

slope =______________

speed = _______________

Slower less slope

A. Graph of d vs. t

What would the graph of a slower object look like?

________d in each _____

How much slower is B?1 2

velocity

d/t speed v

constant

constantsame t

half the speed of A

v

t

A

B

B. Graph of speed __________ for uniform motion

slope =______

aslope =________________

a =_________

B is slower lower

What does the area shown represent?

area = L x W = _____________ =_____________

units: ______ x ______ = _________

What about B?

v vs. t

v/t

slope =______constant = 0

0

speed x time distance

[m/s] [s] [m]

a

t

C. Graph of a vs. t for uniform motion

In review: for __________________ Motion:

d

t

A

B

t

v AB

a

t

a = 0

Same.

a = 0

How would you graph B?

Uniform

paper

tape constant v

timer marks the tape at constant ________ intervals

As car moves, describe pattern of marks on tape.

Ex: tape timers

_____________ spaced b/c car moves the __________ d between each mark.

timer

cart pulls tape________________

time

through timer

How would tape look if car was twice as fast?

Equallysame

III. Non-uniform motion: ___________________ acceleration

d

t

slope of tangent is the______________________

The slope ___________

b/c speed v ___________

A. Graph of d vs. t for object beginning at rest

0

1

2

Object covers ________ din each________________

dashed linesare__________

constant (non-0)

t interval

more

increases

increases

instantaneous v

tangents

________speed vi = ___ __________________

initial 0slope = 0 at t = 0

v

t

B. Graph of speed v vs. t for __________________acceleration a beginning _______________ .

slope =________

= __________

slope = _______________

a = ______________

What does the area shown represent?

area = (1/2) bh = (½) ______________=__________

units: ______ x ______ = ______

constant (non-0)at rest

v/t

accel. a

constant ≠ 0

constant

time x speed distance

[s] [m/s] [m]

a

t

C. Graph of a vs. t for constant a

a = constant

In review: For _________________________acceleration

d

t

v

t

a

t

constant, non-zero

cartpaper

tapeconstant a

As car moves, describe pattern of marks on tape.

Ex:

_______________ spaced b/c car moves _________distance d between each mark.

Timer tape for ___________________

Un-equally

How would tape look if car had more acceleration?

more

constant a

timer

Compare ____________ to ________________motion:

d

t t

v a

t

d

t

v

t

a

t

Uniform

Accel.

slope = v slope = a

area = d

area = d

uniform accelerated

Ex. Answer the questions based on the graph atright.

d (m)

4

2 4 6t (s)

-8

What is the total distance traveled?

What is the resultant displacement?

8 + 8 + 4 = 20 m

+4 m

Find the average speed in the first 2 s.

Find the average speed over the entire 6 s.

Find the average velocity over the entire 6 s.

0

8 m2 s

20 m6 s

+4 m6 s

Ex: The graph below describes a UFO moving in a straight line.

A B

C

Find vavg, d, and a in regions A, B and C.

t (s)

v(m/s)

4.0 8.0 12

20.

40.

In A: v = vi + vf

2

= 30. m/s

v = d/t

d = v t = (30. m/s)(4.0 s)

= 120 m

= area in A

a = Δv/t

= (vf – vi)/t

= (20. m/s + 40. m/s) / 2

= (40. m/s – 20. m/s) / 4.0 s

= 5.0 m/s/ s = 5.0 m/s2

In B: v = vi + vf

2

= 40. m/s

v = d/t

d = v t = (40. m/s)(6.0 s)

= 240 m

= area in B

a = Δv/t

= (vf – vi)/t

= (40. + 40.) / 2

= (40. m/s – 40. m/s) / 6.0 s

= 0

In C: v =

= 20. m/s

d = v t = (20. m/s)(2.0 s)

= 40. m

= area in ΔC: ½bh

a = Δv/t

= (vf – vi)/t

(40. + 0) / 2

= (0 m/s – 40. m/s) / 2.0 s

= -20. m/s2

= v

240 m

t (s)4.0 8.0 12

v(m/s)

20.

40.

A B

C

area = d

a= slope

Which area, A, B or C, is uniform motion?

Which area, A, B or C, is the accelerationconstant, but not zero?

120 m

40 m

Where is the acceleration NOT constant?