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A ball starts with velocity 0 and accelerates down a ramp of length 30 cm, covering the distance in 5 seconds.
• What is its average velocity?
o 30 cm/ 5 sec = 6 cm/s
• If the acceleration of the ball is uniform then its average velocity is equal to the average of its initial and final velocities.
o This statement is correct because we know that the final velocity is equal to the average velocity multiplied by 2 when the initial velocity is 0. When we work this out and manipulate the equation we see that the average of the initial and final velocities is equal to the average velocity.
0 + 12 cm/s = 12/2 = 6 cm/s
• You know its average velocity, and you know the initial velocity is zero. What therefore must be the final velocity?
o The final velocity is equal to the average velocity multiplied by 2 when the initial velocity is 0. Therefore, the final velocity is
6 cm/s * 2 = 12 cm/s.
• By how much did its velocity therefore change?
o The velocity changed by 6 cm/s if the average is 6 cm/s and the final is 12 cm/s. I simply subtracted to obtain the answer.
You have found your change in velocity by subtracting the average velocity from the final velocity. This is not correct.
'What is the initial velocity on this time interval?
What is the final velocity?
How long does the time interval last?
What therefore is the average rate of change of velocity with respect to clock time?
How does this change your result for the average rate of change of velocity with respect to clock time?
• At what average rate did its velocity change with respect to clock time?
o 6 cm/s / 5 s = 1.2 cm/s/s
• What would a graph of its velocity vs. clock time look like? Give the best description you can.
o Velocity would be labeled on the y-axis and clock time would be labeled on the x-axis. The graph would show a diagonal straight line, beginning at velocity 0, because the velocity is increasing at a constant rate.
Good. This line also has a slope. What would be the slope, and what is its meaning?
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20 min
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