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Phy 121
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A ball accelerates uniformly as it rolls 20 cm down a ramp, starting from rest, in 2 seconds.
• What are its average velocity, final velocity and acceleration?
answer/question/discussion: ->->->->->->->->->->->-> :
The average velocity is the change in position divided by the time
20cm / 2s = vAve 10cm/s
The final velocity is 20cm/s if we assume that the initial velocity is 0 because
F0 (0) + fv (20) / 2 = 10cm/s
This also tells us the change in velocity because the product of vAve and `dt = `dv.
Our change in velocity divided by our change in time gives us acceleration
(20cm/s) / 2sec = 10cm/s^2
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• If the time interval is in error so that it is 3% longer than the actual time interval, then what are the actual values of the final velocity and acceleration?
answer/question/discussion: ->->->->->->->->->->->-> :
Final velocity is 20cm/s - (3%) = 19.97
Acceleration is 10cm/s - (3%) = 9.97
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The change in velocity, which is based on the calculation of average velocity, is 3% less. Then you divide by the new time interval, which is 3% longer. This doesn't result in a 3% uncertainty.
Note also that 3% less than 20 is 19.4, not 19.97.
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• What is the percent error in each?
answer/question/discussion: ->->->->->->->->->->->-> :
The percent error for the final velocity is 0.03/19.97 *100 = 0.15 percent
The percent error for the acceleration is 0.03 / 9.97 *100 = 0.3 percent
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These also need revision.
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