Plot and interpret position-time graphs

• A position time graph shows an objects change in position over a period of time.

Plot and interpret position-time graphs (cont’d)

• An object which is moving at a constant velocity would cover equal distances in equal amount of time and it’s graph would appear as an upwardly sloping diagonal line.

d

t

Constant Velocity

Plot and interpret position-time graphs (cont’d)

• An object which is moving with a constant acceleration will cover larger and larger distances in successive equal time intervals. Its position time graph would appear as a curve.

d

t

Constant Acceleration

Calculate the velocity of an object from a position time

graph

• The slope of the position time graph is the velocity of the object.

x

ym

run

riseSlope is calculated using or

Calculate the velocity of an object from a position time

graph

0102030405060708090

100

0 1 2 3 4 5

Posi

tion

(m)

Time (sec)s

mv

s

mv

s

mmv

20

4

804

1090

Plot and interpret a velocity-time graph

• An object which is moving with a constant acceleration will have a velocity time graph that is an upwardly sloping diagonal line. The y-intercept is the initial velocity of the object.

v

t

Constant Positive Acceleration

Calculate the acceleration of an object from a velocity time

graph• The slope of the velocity time graph is the

acceleration of the object.

x

ym

run

riseSlope is calculated using or

Calculate the acceleration of an object from a velocity time

graph

02468

101214161820

0 1 2 3 4 5

Velo

city

(m/s

)

Time (sec)

22

5

10

05

414

s

ma

ssm

a

sssm

sm

a

Calculate the displacement from a velocity time graph

• The area between the velocity time graph and the x-axis is the displacement of the object during that time interval.

Sample Problem

• What is the displacement of the object during the first 5 seconds?

0

2

4

6

8

10

12

14

0 5 10 15 20 25

Time (sec)

Velo

city

(m/s

)

Sample Problem (cont’d)

0

2

4

6

8

10

12

14

0 5 10 15 20 25

Time (sec)

Velo

city

(m/s

)

• The area that needs to be analyzed is the green triangle. The area of a triangle can be calculated using

bha2

1

Sample Problem (cont’d)

0

2

4

6

8

10

12

14

0 5 10 15 20 25

Time (sec)

Velo

city

(m/s

)md

s

msd

10

452

1

Plot and interpret an acceleration-time graph

• An object which is moving with constant acceleration would graph as a horizontal line above the x-axis. The y-intercept would be equal to the value of the acceleration.

a

t

Constant Acceleration

Constant Acceleration