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15 June, 12:50

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?

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  1. 15 June, 15:02
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    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!
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