course PHY 201
9/15 10:29 pm
If the velocity of the object changes from 5 cm / sec to 15 cm / sec in 9 seconds, then at what average rate is the velocity changing?vvvv
The change in the velocity is 10 cm in 9 seconds. To get the average rate at which the velocity is changing you would divide the change in velocity by the time, which would be 10/9 = 1.1 cm/s
10 cm is not a change in velocity; a change in velocity would have units of velocity.
The main point of my note is that you are using the right procedure, but your units are wrong.
A ball rolling from rest down a constant incline requires 3.9 seconds to roll the 49 centimeter length of the incline.
• What is its average velocity?
vAve = `ds / `dt
vAve = 49 cm / 3.9 s = 13cm/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?
fVel = 2*(vAve)
fVel = 2*13
fVel = 26 cm/s
• What average rate is the velocity of the ball therefore changing?
(26 cm/s) / (13cm/ s) = 2cm/s
The average rate of change of velocity with respect to clock time is not final velocity / average velocity.
An automobile accelerates uniformly down a constant incline, starting from rest. It requires 13 seconds to cover a distance of 110 meters. At what average rate is the velocity of the automobile therefore changing?
vAve= `ds/ `dt
vAve = 110m / 13s
vAve = 8.5 m/s
This is the average velocity, but it's not the average rate at which the velocity is changing.
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Solution
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