#$&*
course Phy 241
10/02/2011 around 4:30 AM
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?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?
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?
What average rate is the velocity of the ball therefore changing?
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?
Solution:
The velocity will be changing at the average rate of
(16cm/sec-4cm/sec)/8sec = (12cm/sec)/8sec = 1.5cm/sec/sec.
For a ball rolling down, the average velocity is = 97cm/8.2sec = 11.83cm/sec.
@& Good so far, but you don't go on to find the final velcocity or the average rate of change of this ball's velocity.*@
We will get the average velocity first which is change of position divided by change of the time clock. Once we get the average velocity we multiply it by two to get the final velocity.
The average rate will be the difference in initial velocity from the final velocity divided by the time it took for the travel.
The average rate is 132 meters/10sec = 13.2 meters/sec"
@& This is the average rate of change of the position with respect to clock time, not the average rate of change of velocity with respect to clock time.*@
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