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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?
If the length is 30cm then you would go 30cm/ 5s to determine the Vave. This means Vave= 6cm/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?
Vave=(Vo+Vf/2)*’dt With this formula you are able to use algrebra to manipulate it into figuring out that 6x2gives 12cm/s for the Vf
• By how much did its velocity therefore change?
‘dv=vf-v0 with this formula you just go 12cm/s-0cm/s we see that velocity changed 12cm/s
• At what average rate did its velocity change with respect to clock time?
6cm/s
This is the average velocity. Follow, step by step, the definition of average rate of change of velocity with respect to clock time.
• What would a graph of its velocity vs. clock time look like? Give the best description you can.
It would be increasing at an increasing rate
For some ramps it would be so. For some it would not--the graph could be a straight line or it could increase at a decreasing rate. It could be even more complicated than that. You can't tell from the given information.
If you assume that the velocity increases, the the position vs. clock time graph would increase at an increasing rate.
A description of the v vs. t graph might start with the known points on the graph. You know the coordinates of two points. What are they?
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30min
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