#$&*
course phy 121
A ball accelerates uniformly as it rolls 20 cm down a ramp, starting from rest, in 2 seconds. What are its average velocity, final velocity and acceleration?
answer/question/discussion:
vAve = 20cm/2s = 10cm/s
Final velocity = 20cm/s
Acceleration= 20cm/s / 2s = 10cm/s/s
#$&*
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:
time interval = 2s + (2s*.03) = 2.06s
vAve = 20cm/2.06s = 9.7cm/s
9.7cm/s = (v0+vf) / 2
Vf = 19.4cm/s
Acceleration = 19.4cm/s / 2.06s = 9.4cm/s/s
#$&*
What is the percent error in each?
answer/question/discussion:
Final velocity percent error: 19.4cm/s - 20cm/s / 20cm/s = 3%
Acceleration percent error: 9.4cm/s/s - 10cm/s / 10cm/s = 6%
#$&*
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:
They are different because with the final velocity, only one part of it is changing (2.06s). The acceleration changes in two aspects, which are the new final velocity as well as the new time (2.06s). Therefore, the percent error has no chance to be the same. If the percent error were to be the same in both cases, there would have to be a different part of each of these problems changing (ie: not the time).
&#Very good work. Let me know if you have questions. &#