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course Phy 241
If the velocity of the object changes from 3 cm / sec to 13 cm / sec in 7 seconds, then at what average rate is the velocity changing?
(13cm-3cm)/(7sec-1sec) = 10cm/6sec = 5cm/3sec
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5/3 cm/s is not a rate at which velocity changes. It doesn't have the correct units.
13 cm and 3 cm are distances or positions, and are not quantities associated with this question.
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A ball rolling from rest down a constant incline requires 4.6 seconds to roll the 54 centimeter length of the incline.
What is its average velocity?
54cm / 4.6 seconds ~ 11.74cm/sec
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?
11.74cm/sec * 2 = 23.48cm/sec
What average rate is the velocity of the ball therefore changing?
Since we started at a stand still, our average rate is 11.74 cm/sec
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This is the average rate at which the position is changing, not the average rate at which the velocity is changing.
Go back to the definition of average rate and be sure you think through every step.
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An automobile accelerates uniformly down a constant incline, starting from rest. It requires 14 seconds to cover a distance of 106 meters. At
what average rate is the velocity of the automobile therefore changing?
106 meters / 14 seconds = 7.57m/sec
7.57 m/sec is our average velocity and our average rate since we started from a stand still."
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This is the average rate at which the position is changing, not the average rate at which the velocity is changing.
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