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