course Phy 231
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?
Average rate of change of velocity: (16 cm/s – 4 cm/s) / 8 s = 12 cm/s / 8s = 1.5 cm/s^2
Average velocity: vAve = 97 cm / 8.2 s = 12 cm/s
Final velocity = 2*vAve = 2 * 12 cm/s = 24 cm/s
Average rate of change of velocity: 24 cm/s / 8.2 s = 2.9 cm/s^2
Average velocity: 132 m / 10 s = 13.2 m/s
Final velocity: 2 * 13.2 m/s = 26.4 m/s
Average rate of change of velocity: 26.4 m/s / 10 s = 2.64 m/s^2
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