course PHY 121
6/29 10p
If the velocity of the object changes from 4 cm / sec to 16 cm / sec in 8 seconds, then at what average rate is the velocity changing?16 cm/s - 4 cm/s = 12 cm/s is the `dv, divide this by `dt giving 12cm/s / 8 s = 1.5 cm/s^2.
A ball rolling from rest down a constant incline requires 8.2 seconds to roll the 97 centimeter length of the incline.
What is its average velocity? vAve = `dy/`dt or 97cm/8.2s, giving vAve = 11.83 cm/s.
An object which accelerates uniformly from rest will attain a final velocity which is double its average velocity.
What therefore is the final velocity of this ball? 23.66 cm/s.
What average rate is the velocity of the ball therefore changing?
Change in velocity/change in time in this case would be 23.66/8.2 = 2.89 cm/s^2.
An automobile accelerates uniformly down a constant incline, starting from rest. It requires 10 seconds to cover a distance of 132 meters. At what average rate is the velocity of the automobile therefore changing?
vAve = `dy/`dt, giving vAve = 132/10, giving vAve 13.2 m/s.
Final velocity will be vAve * 2, giving a final velocity of 26.4 m/s.
using the standard rate formula then, `dy / `dt with final velocity as the change in y and the total time of 10 s, 26.4/10, resulting in a 2.64m/s/s change in velocity.
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