Phy 121
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The problem:
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?
answer/question/discussion: If it travels 30 cm in 5 seconds then it would be traveling at a rate of (30cm/5sec) = 6cm/sec.
Since there are no other time intervals to compare distance to then there is only the average of the beginning and ending velocities.
• If the acceleration of the ball is uniform then its average velocity is equal to the average of its initial and final velocities.
answer/question/discussion: True?
• You know its average velocity, and you know the initial velocity is zero. What therefore must be the final velocity?
answer/question/discussion: The two velocities must be averaged together
vf = v0 + a * `dt
30cm/sec = ( 0 + 6cm/sec) * 5cm/sec
• By how much did its velocity therefore chang
There is no quantity in this problem that is equal to 30 cm/s, which is a velocity. There is a displacement of 30 cm, but this is not a final velocity.
v0 + a * `dt is different than (v0 + a) * `dt; the latter is not a correctly formed expression, since v0 and a have different units and are therefore unlike terms which cannot be added.
6 cm/s is not an acceleration in any case.
answer/question/discussion:
av = [(vf + v0) / `dt
6cm/sec/ = (30cm / 5sec)
neither vf nor v0 has units of cm, so (vf + v0) could not be 30 cm.
What specific steps are required to solve the equation a_Ave = v0 + a `dt for a?
None it was increasing at a constant rate.
• At what average rate did its velocity change with respect to clock time?
answer/question/discussion:
av = [(vf + v0) / 2] / `dt
(vf + v0) / 2 is the average of the initial and final velocities and is not related to acceleration.
What is the definition of acceleration? How is it therefore related to initial and final velocity and time interval?
1.2cm/sec/sec = (6cm/sec /2) / 5sec
• What would a graph of its velocity vs. clock time look like? Give the best description you can.
answer/question/discussion: The graph would be increasing at an increasing rate.
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1hr 30 mins
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You have the right general ideas, but you need to be clearer on the specifics.
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