A particle of mass m starts from rest and is driven by a machine that supplies a constant power k (in watts). What is the force acting on the particle at time t?

sqrt(2mk) * t^(-1/2)
(1/2) * sqrt(mk) * t^(-1/2)
sqrt(mk/2) * t^(-1/2)
sqrt(mk) * t^(-1/2)

Correct answer: sqrt(mk/2) * t^(-1/2)

Solution

Since power P = k is constant and particle starts from rest, work done = kt = (1/2)mv², giving v = sqrt(2kt/m). Force F = P/v = k / sqrt(2kt/m) = k * sqrt(m/(2kt)) = sqrt(mk² / (2kt)) = sqrt(mk/(2t)) = sqrt(mk/2) * t^(-1/2).

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