aim: how can we determine acceleration on a distance-time graph? do now: determine the displacement...

Aim: How can we determine acceleration on a distance-time

graph?

Do Now:

Determine the displacement of the following graph:

AB

C

D E-5

-4

-3

-2

-1

0

1

2

3

4

5

0 1 2 3 4 5 6 7 8 9 10 11

time (s)

velo

city

(m

/s)

d = bh = (5 s)(5 m/s) = 25 m

d = ½bh = ½(2 s)(5 m/s) = 5 m

d = ½bh = ½ (2 s)(-5 m/s) = -5 m

d = bh = (2 s)(-5 m/s) = -10 m

Total displacement = 15 m

Describe the motion on the following distance-time graph:

A

B

C

D Constant positive slope = constant velocity forward

Curved line = changing slope = acceleration

Positive slope = forward =accelerating foward

Constant positive slope = constant velocity forward

Is the object speeding up or slowing down?

•Determine if the slope is increasing or decreasing

A

B

C

D

Slop

e 1 Slope 2Slope 2 is less steep than slope 1

This means that slope 2 is moving with a slower velocity

In other words, the object is slowing down

Since the slope is still positive, the object is mowing forward

Slowing down forward

Slope 1

Slope 2

•Slope 2 is steeper than slope 1

•Both slopes are positive

Speeding up forward

Slope 1

Slope 2

•Slope 2 is steeper than slope 1

•Both slopes are negative

Speeding up backward

Slope 1

Slope 2

•Slope 2 is less steep than slope 1

•Both slopes are negative

Slowing down backward

Describe the motion on the following distance-time graph:

distance

time

A B

C

D

E F

G

H

I J

__

AB: At rest

__

BC: Speeding up forward

__

CD: Constant velocity forward

__

DE: Slowing down forward

__

EF: At rest

__

FG: Speeding up backward

__

GH: Constant velocity backward

__

HI: Slowing down backward

__

IJ: At rest

Instantaneous Velocity

This is velocity at a specific moment in time

On a distance-time graph:

Find the slope of the line on the graph using points one second before and one second after the time indicated

Find the instantaneous velocity at 14 seconds

0

20

40

60

80

100

120

140

160

13 14 15

time (s)

dis

tan

ce (

m)

If you just went 100m/14s, you would get an incorrect answer!

On a velocity-time graph

Just read the graph

0

5

10

0 1 2 3 4 5 6 7

time (s)

velo

city

(m/s

)

What is the instantaneous velocity at:

1 s

5 m/s

3 s

5 m/s

5 s

10 m/s