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A time dependent force $F = 3 t^{2} + 6 t$ acts on a particle of mass 18 kg. If particle starts from rest, the work done by the force during the first 3 second, will be

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40.5 J

324 J

81 J

262 J

answer is C.

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Detailed Solution

Change in momentum
$\begin{array}{l} ΔP = \int_{0}^{t} Fdt \\ ΔP = \int_{0}^{3} (3 t^{2} + 6 t) dt = 54 \\ P - 0 = 54 \\ P = 54 \\ ΔK = \frac{P^{2}}{2 m} = \frac{54 \times 54}{2 \times 18} = 81 J \end{array}$

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