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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: ->->->->->->->->->->->-> :
Using the equation ds = (v0 +vf)/2 *dt = the final velocity is 20cm/s so the average velocity is 10m/s. Using the equation vf = v0+adt, acceleration is 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: ->->->->->->->->->->->-> :
Time interval is actually 1.04 seconds, so the final velocity is 38.46 c/m, the average velocity is therefore 19.2 cm/s, and the acceleration is 36.9 cm/s^2.
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• What is the percent error in each?
answer/question/discussion: ->->->->->->->->->->->-> :
Final Velocity = 48%
Acceleration = 72%
Average Velocity = 48%
The error in final velocity according to your calculation is 1.5 cm/s, which is a little less than 4% of the 40 cm/s you would be assuming here. So the percent error would be 4%.
However the time interval would not be 1.04 seconds. A 3% error on an interval of 2 seconds would correspond to an interval of 2.06 seconds.
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• If the percent error is the same for both velocity and acceleration, explain why this must be so.
answer/question/discussion: ->->->->->->->->->->->-> :
I didn’t get the same value for both acceleration and velocity, but they do have a linear relationship, if the acceleration speeds up, the velocity increases. Since they are in a away dependant on each other and have a direct relationship, any differences should have the same percent error.
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• If the percent errors are different explain why it must be so.
answer/question/discussion: ->->->->->->->->->->->-> :
They are different, because even though they are related, in a sense, if the length of the distance traveled changes then the velocity would change without the acceleration changing.
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15 minutes
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