Acceleration is the rate of change of velocity. The velocity (positive means down) of a pumpkin thrown off the top of Cheadle hall t seconds after launch is 32t ft/sec (until it hits the ground). (a) What is the average rate of change of velocity between t=1 and t=2?

The average rate of change of velocity is 32 ft/s²

Explanation:

Hi there!

The velocity in fuction of t is v (t) = 32 · t

At t = 1 s, the velocity will be v (1) = 32 · 1 = 32 ft/s

At t = 2 s, the velocity will be v (2) = 32 · 2 = 64 ft/s

The average rate of change of the velocity can be calculated as follows:

Rate of change of velocity = Δv/Δt

Where:

Δv = final velocity - initial velocity

Δt = final time - initial time

In our case:

final velocity = 64 ft/s

initial velocity = 32 ft/s

Final time = 2 s

initial time = 1 s

Then:

Δv/Δt = (64 ft/s - 32 ft/s) / (2 s - 1 s) = 32 ft/s²

Then, the average rate of change of velocity is 32 ft/s². It means that the velocity of the pumpkin will increase 32 ft/s per second.

Have a nice day!