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course Phy 231

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:

Answer: ave vel = ds/dt = 20cm / 2s = 10cm/s. since v0 = 0cm/s, vf = 20cm/s. dv = 20cm/s, acc = 20cm/s / 2s = 10cm/s/s.

?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:

Answer: If the time is actually 3% longer than previously reported, the actual time would be 2.06s. ave vel = 20cm / 2.06s = 9.71cm/s. vf = 19.42cm/s, dv = 19.42cm/s, acc = 19.42cm/s / 2.06s = 9.43cm/s/s.

?What is the percent error in each?

answer/question/discussion:

Answer: vf % error: (20cm/s ?19.42cm/s) / (19.42) * 100% = 3%. Acc % error: (10cm/s/s ?9.43cm/s/s) /(9.43cm/s/s) * 100% = 6%.

?If the percent error is the same for both velocity and acceleration, explain why this must be so.

answer/question/discussion:

?If the percent errors are different explain why it must be so.

answer/question/discussion:

Answer: To find the acceleration, you use dt twice, once to find the dv and another to divide dv by dt. Since dt has a percent error of 3% and you are using it twice, there will be a 6% error in the acceleration.

Good.