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course phy 121
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?
The average rate of change is 'dv / 'dt = 16 cm/sec - 4 cm/sec = 12 cm/sec
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'dv = 16 cm/sec - 4 cm/sec = 12 cm/sec
'dv / 'dt = (16 cm/sec - 4 cm/sec) / (8 s) = 12 cm/sec / (8 s) = 1.5 cm/s^2,
the latter of which agrees with the result you obtain below.
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12 cm/sec / 8 seconds = 1.5 cm/sec / sec or 1.5 cm/sec^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?
v_ave = 'ds/'dt = 97 cm / 8.2 sec = 11.83 cm/sec Assuming 2 sig figures rounds to 12 cm/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?
v_ave = 12 cm/sec so, v_f = 12 cm/sec
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A ball with initial velocity 0 and final velocity 12 cm/s has average velocity 6 cm/s.
You'll need to reconsider this answer, and its implications for subsequent answers.
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What average rate is the velocity of the ball therefore changing?
Acceleration = 'dv/'dt where 'dv = v_f - v_0 ; 'dv = 24cm/sec
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You probably just typed your vf incorrectly in the preceding. Otherwise you wouldn't have obtained `dv = 24 cm/s, which is the correct result for `dv.
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24 cm/sec / 8.2 sec = 2.9 cm/sec/sec
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Good.
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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?
'ds/'dt = 132 meters / 10 seconds = 13.2 m/s
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This is the average rate of change of position with respect to clock time, not the average rate of change of velocity with respect to clock time.
You will need to revise your solution on this question.
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