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course Phy 201
If the velocity of the object changes from 3 cm / sec to 15 cm / sec in 10 seconds, then at what average rate is the velocity changing?The average rate equation is defined as the change in a divided by the change in b, here a is the change in velocity and b is the change in time. The velocity is changing at an average rate of:
=(15cm/s - 3cm/s)/10s
=1.2cm
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You are using the right relationship, and the right quantities are in the right places.
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12 cm/s / (10 s) has a numerical value of 1.2, but (cm/s) / s does not give you cm, nor is this a unit appropriate to rate of change of velocity with respect to clock time.
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A ball rolling from rest down a constant incline requires 4.4 seconds to roll the 86 centimeter length of the incline.
What is its average velocity?
vAve=delta s/ delta t
=86cm/4.4s
=19.54cm/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?
The average velocity of a uniformly accelerating object that starts from rest (only) will have an average velocity that is half it’s final velocity. Doubling the average velocity, 19.54cm/s, gives 39.09m/s, the final velocity.
What average rate is the velocity of the ball therefore changing?
I’m not sure I know how to do this without being given a time, but here I will double the time since we doubled the velocity. The velocity of the ball is changing at an average rate of : (39.09cm/s-19.54cm/s)/(8.8s)=2.2cm
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You're on the right track.
How much did the velocity change during the entire interval specified in the problem?
By how much did the clock time change?
What therefore is the requested average rate?
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Do be careful about the units of your calculation.
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An automobile accelerates uniformly down a constant incline, starting from rest. It requires 10 seconds to cover a distance of 138 meters. At what average rate is the velocity of the automobile therefore changing?
vAve=delta s/ delta t
vAve=138m/10s
vAve=13.8m/s
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This is the average rate of change of position with respect to clock time.
This is useful, but you were asked for the average rate of change of velocity with respect to clock time.
The reasoning of the preceding questions are relevant to the solution of this problem as well.
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