1. Motion Graphs – Area Under the Graph

2. Area Under the Graph in Kinematics
Velocity is the rate of change of position, i.e. how fast position changes over time. or
Acceleration is the rate of change of velocity, i.e. how fast velocity changes over time. or

3. Example 1
A bus travels on a northbound street for 20.0 s at a constant velocity of 10.0 m/s. After stopping for 20.0 s, it travels north at a constant velocity of 15.0 m/s for 30.0 s to the next stop, where it remains for 15.0 s. For the next 15.0 s, the bus continues north at 15.0 m/s.
Draw the graph of velocity vs. time.
Calculate the partial displacements.
Draw the graph of position vs. time.

4. Example 1 Draw the graph of velocity vs. time.
v (m/s)
∆t (s)
∆x (m)
0-20
200
20-40
40-70
450
70-85
85-100
225
t (s)
b. Calculate the partial displacements.

5. Example 1 c. Draw the graph of position vs. time.
x (m)
∆t (s)
∆x (m)
0-20
200
20-40
40-70
450
70-85
85-100
225
t (s)
How would you get the graph of
velocity vs. time from the graph above?

6. Example 2
An athlete is practicing inside a gym. She runs forward for 2.0 s at a constant speed of 2.0 m/s. During the next 2.0 s she decelerates to a complete stop. Then for another 2.0s she accelerates backwards up to a speed of 2.0 m/s.
Draw the graph of velocity vs. time.
Calculate the displacement for the first 4 seconds.
Calculate the total displacement.
Calculate the acceleration (both magnitude and direction) for the interval s.

7. Example 2 Draw the graph of velocity vs. time. b. Interval 0-4s:
c. Interval 4-6s:
d. Interval 2-6s: