Name: _____________________________
KLesson8: Velocity vs. Time
Date: _________
Period: _______
Lesson 8: Using Velocity-versus-Time Graphs to find
Displacement
8.1 Represent and Reason
The figure on the right shows a velocity
versus- clock reading graph that represents
the motion of a bicycle, modeled as a point
particle (we are not interested in the motion
of the feet, head, etc.), moving along a
straight bike path. The positive direction of
the position axis is toward the east.
a) Describe the motion of the bike in words.
b) How is this graph different from the
position versus time graph for the same motion?
c) Think of how you can use the graph to estimate the bike’s displacement from a clock reading of 10 s
to a clock reading of 15 s. Explain. (Hint: Think of the area of a rectangle.)
d) Use the graph to estimate the bike’s displacement from a clock reading of 0 s to 20s.
e) Formulate a general rule for using a velocity versus clock reading graph to determine an object’s
displacement during some time interval if the object is moving at constant velocity.
f) Is this rule consistent with the mathematical models developed in the previous lessons: x = vt + xi
for constant velocity?
8.2 PHYSICS CP– SKETCHING MOTION GRAPHS
Use the following position-time graph to sketch a velocity-time graph that shows the same motion.
Position-Time Graph 1
8
6
4
Position (m)
2
0
-2
-4
-6
-8
0
2
4
6
8
10
12
8
10
12
Time (s)
Velocity-Time Graph 1
4
3
2
Velocity (m/s)
1
0
-1
-2
-3
-4
0
2
4
6
Time (s)
8.3 Represent and Reason
a) Bike A started moving at constant positive velocity.
b) Bike B climbed over a flat hill.
c) Bike A stopped twice during the trip.
d) Bike B stopped twice during the trip.
e) The last part of the trip bike A was not moving.
f) The last part of the trip bike B was moving at constant speed in the negative direction.
g) The last part of the trip bike A was moving at constant speed in the negative direction.
h) When we started observing Bike B it was moving at constant positive velocity.
i) When we started observing bike A it was moving at increasing velocity in the positive direction, then
it reached some constant velocity (positive) and continued moving for a while, then its velocity started
decreasing and it some point it became zero. Then it continued to increase in the negative direction
until it reached some new velocity which it maintained for a while.
j) When we started observing bike B it was moving at constant velocity in the positive direction, then it
stopped for a while, then it started going back to the origin and then in the negative direction. Finally it
stopped.
8.4 Evaluate
Examine the graphs below. Then choose the statements with which you disagree. Explain your reasons.
Then explain why someone would choose those wrong answers as correct.
a) The first two graphs (A and B) provide the same information.
b) The second two graphs (C and D) provide the same information.
c) Object A traveled 60 meters in 3 seconds from the location it was at the 0 clock reading.
d) Object B traveled 40 meters in 2 seconds in the positive direction.
e) Object C was not moving during the experiment.
f) Objects A and D were not moving during the experiment.
g) Object C was moving in the negative direction at the speed of 20 m/s.
h) Object D was moving in the negative direction at the speed of 20 m/s.
i) Object C was moving in the negative direction at the speed of (-20 m/s).
j) Object D traveled 40 m in 2 seconds in the negative direction.