Phy 121
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The problem:
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: ->->->->->->->->->->->-> :
`dv = `ds / `dt = (30 cm) / (5 s) = 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.
You know its average velocity, and you know the initial velocity is zero.
What therefore must be the final velocity?
answer/question/discussion: ->->->->->->->->->->->-> :
vAve = (vInitial + vFinal) / 2
2(vAve) = vInitial + vFinal
2(vAve) – vInitial = vFinal
2(6 cm/s) – (0 cm/s) = vFinal
12 cm/s = vFinal
• By how much did its velocity therefore change?
answer/question/discussion: ->->->->->->->->->->->-> :
`dv = vFinal – vInitial = (12 cm/s) – (0 cm/s) = 12 cm/s
The velocity changed by 12 cm/s
• At what average rate did its velocity change with respect to clock time?
answer/question/discussion: ->->->->->->->->->->->-> :
`dv = rate of `dv * `dt
12 cm/s = rate of `dv * (5 s)
(12 cm/s) / (5 s) = rate of `dv
2.4 cm/s = rate of `dv
• What would a graph of its velocity vs. clock time look like? Give the best description you can.
answer/question/discussion: ->->->->->->->->->->->-> :
The x-axis represents clock time and the y-axis represents velocity. As more time passes, the ball moves faster. The graph is exponential and increasing at an increasing rate.
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15 minutes
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Very good. Do, however, check the discussion of units at the link.
&#Please compare your solutions with the expanded discussion at the link
Solution
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