Worksheet
Accelerated Motion: Analyzing Velocity-Time Graphs
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Refer to the following information for the next six questions.
Match the description provided about the behavior of a cart along a linear track to its best graphical representation. Remember that:
velocities are positive
when the graph is in I quadrant I
velocities are negative
when the graph is in quadrant IV
velocity-time graphs sloping towards the x-axis represent
losing speed
velocity-time graphs sloping away from the x-axis represent
gaining speed
the slope of a velocity-time graph represents its
acceleration
moving in a negative direction and losing speed
A
B
C
D
no match
moving in a positive direction and gaining speed at a slow rate
A
B
C
D
no match
traveling at a steady rate in a positive direction
A
B
C
D
no match
at rest for an extended time
A
B
C
D
no match
moving in a positive direction but losing speed
A
B
C
D
no match
moving in a positive direction and gaining speed at a rapid rate
A
B
C
D
no match
Refer to the following information for the next two questions.
Given below is a velocity-time graph displaying the behavior of a race cart along a linear track.
During which time interval(s) did it travel in a positive direction?
0-10 min
10-15 min
15-30 min
30-40 min
40-55 min
During which time interval(s) did it travel in a negative direction?
0-10 min
10-15 min
15-30 min
30-40 min
40-55 min
Refer to the following information for the next eight questions.
Using the same velocity-graph as in section two above, answer these questions regarding how far the cart traveled, its average speeds during each interval, and its displacement. Remember that:
velocity
is determined by the height of the graph (the y-axis coordinate)
acceleration
is determined by the slope of the graph
displacement
is found by calculating the area bounded by the velocity-graph and the x-axis
distance traveled
would be the absolute value of each sectional area since it is a scalar quantity that does not depend on the direction of travel
average speed
during a time interval is defined as the total distance it traveled divided by the total time taken
average velocity
during a time interval is defined as the net displacement divided by the total time taken
How far did the cart travel in the first 10 minutes? What was its average acceleration during this time interval?
Briefly describe its behavior between 10 and 15 minutes?
What was its average acceleration between 10 and 15 minutes?
How far did it travel between 15 and 30 minutes? What was its average acceleration during this time interval?
How far did it travel between 30 and 40 minutes? What was its average acceleration during this time interval?
How far did it travel between 40 and 55 minutes? What was its average acceleration during this time interval?
What was the total distance it traveled? What was its final displacement?
What was the cart's average speed for the entire 55 minutes? its average velocity?
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