course Phy 241
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A ball rolling from rest down a constant incline requires 8.2 seconds to roll the 97cm length of the incline. What is its average velocity?
Average velocity can be found by dividing the distance rolled by the time interval. 97cm/8.2 sec is approximately 12 cm/sec.
What is the final velocity?
We already calculated the average velocity which is about 12 cm/sec, so therefore the final velocity is double the average velocity or 24 cm/sec.
What is the average rate velocity is changing?
The average rate which velocity is changing is acceleration. Acceleration can be found by taking the change in velocity which at rest was 0 cm/sec and final was 24 cm/sec, therefore the change is 24 cm/sec. Next this is divided by the change in time 8.2 seconds. (24cm/sec) / 8.2 sec is about 3 cm/sec^2.
An automobile accelerates uniformly down a constant incline, starting from rest. It requires 10 sec to cover a distance of 132 m, at what average is the velocity of the auto therefore changing?
First we can calculate the average velocity by dividing the 132 m by the 10 seconds to yield 13.2 cm/sec. Next we can find the final velocity because acceleration is uniform; therefore final velocity is twice that of the average velocity or 26.4 cm/sec. To find the average acceleration, we take the change in velocity and divide by the change in time. The velocity changes 26.4 cm/sec from 0cm/sec to 26.4 cm/sec. The total time to make this change was 10 sec, therefore the average acceleration is (26.4cm/sec)/10 sec = 2.64 cm/sec^2.
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Excellent solution.