CLASSICAL MECHANICS & THERMODYNAMICS - Chapter 3, Exercise 3 Solution
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Finding Time from Power and Work (P = W/t)

PROBLEM
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A small electric motor can output 150 W of power. How long will it
take the motor to do 4,500 J of work? Give your answer in seconds.

SOLUTION
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Starting from the power equation:

    P = W / t

Rearranged to solve for time:

    t = W / P

Substitute the given values:

    W = 4500 J
    P = 150 W

    t = 4500 / 150
    t = 30 s

ANSWER: The motor takes 30 seconds to do 4,500 J of work.

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WHY THIS WORKS AS AN ANSWER

Power is defined as the RATE at which work is done - joules of work
per second. Rearranging P = W/t into t = W/P simply asks "how many
of those per-second chunks of work does it take to add up to the
total?" A motor outputting a steady 150 J every second needs exactly
30 of those one-second intervals to accumulate the full 4,500 J,
which is exactly what dividing the total work by the power figure
calculates directly.