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?Answer: ((16 cm/sec + 4 cm/sec)/(2)) / (8 sec) = (10 cm/sec)/(8 sec) = 1.25 cm/sec/sec.
You have divided the average velocity by the time interval. This is not the definition of the average rate at which velocity changes with respect to clock time. That definition has nothing to do with average velocity.
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?
Answer: vAve = 97cm / 8.2 sec = 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?
Answer: final velocity = 2 * 12 cm/sec = 24 cm/sec.
?What average rate is the velocity of the ball therefore changing?
Answer: average acceleration =( 24 cm/sec) / (8.2 sec) = 3 cm/sec/sec.
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?
Answer: vAve = 132m/10sec = 13.2 m/sec, final velocity = 26.4 m/sec, average acceleration = (26.4 m/sec)/(10 sec) = 2.64 m/sec/sec.
You have answered all questions correctly except the first. See my note and be sure you understand what you did wrong there; it appears that you confused two definitions, both of which you know quite well.