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PHY 121
Your 'cq_1_03.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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A ball starts with velocity 0 and accelerates uniformly down a ramp of length 30 cm, covering the distance in 5 seconds.
What is its average velocity?
answer/question/discussion: ->->->->->->->->->->->-> n (start in the next line):
vAve = (30cm)/(5sec) = 6cm/sec
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If the acceleration of the ball is uniform then its average velocity is equal to the average of its initial and final velocities.
You know its average velocity, and you know the initial velocity is zero.
What therefore must be the final velocity?
answer/question/discussion: ->->->->->->->->->->->-> n (start in the next line):
vf = 2* (vAve)
=12cm/sec
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By how much did its velocity therefore change?
answer/question/discussion: ->->->->->->->->->->->-> n (start in the next line):
Velocity changed by 12cm/sec
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At what average rate did its velocity change with respect to clock time?
answer/question/discussion: ->->->->->->->->->->->-> n (start in the next line):
aAve = (12cm/sec)/5sec = (2.4cm/sec)/sec = 2.4cm/sec^2
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What would a graph of its velocity vs. clock time look like? Give the best description you can.
answer/question/discussion: ->->->->->->->->->->->-> n (start in the next line):
Since the acceleration was uniform, its graph would be a linear function with a constant slope of 6 beginning at (0 velocity, 0 time).
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10m
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The slope of the graph of velocity vs. time would not be 6. A graph of position vs. clock time, with a constant velocity of 6 cm/s, would have slope 6 cm/s. But this motion is not at constant velocity, and the requested graph is not of position vs. time but of velocity vs. time.
The slope of this graph would be 2.4 cm/s^2. (see also the preceding 'seed' question).
The coordinates of a graph of velocity vs. time would be in the order (time, velocity). This is in fact how you interpreted them in your work on the preceding questions, which is correct throughout.
The initial value of the clock time is not specified, which allows you to assume any initial value for the time. You have assumed 0 sec for the intial time, so that the initial point would be (0 s, 0 cm/s).
So as long as you have the order of the quantities right, (0, 0) could represent the initial point, and with slope 2.4 cm/s^2, rather than 6, your description of the graph would be valid.
It would also be valid for any initial point whose second coordinate (the velocity) is zero. For example, a line starting at (43 sec, 0 cm/s) with slope 2.4 cm/s^2 would also be valid. The only condition for the starting point would be that the velocity coordinate be zero.
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If you understand all this, and I think there's a good chance that you will, you'll find it valuable on future assignments. If you have questions, let me know and I'll be glad to clarify.
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