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CGP EDU Academic Team
Published on: September 12, 2026
A body of mass 3 kg is under a force, which causes a displacement in it is given by $S = t^{4} - 3t^{3}$ (in m). Find the work done by the force in first 2 seconds
Text Solution
Verified by ExpertsThe correct answer is:
D
$S = t^{4} - 3t^{3}$ ∴ ∴ $dS = t^{2} dt$
$a = \frac{d^{2}S}{dt^{2}} = \frac{d^{2}}{dt^{2}}\left[\frac{t^{3}}{3}\right] = 2t \, m/s^{2}$
Now work done by the force $W = \int_{0}^{2} F . dS = \int_{0}^{2} m a . dS$
$\int_{0}^{2} 3 \times 2t \times t^{2} \, dt$ $= \int_{0}^{2} 6t^{3} dt$ = $\frac{3}{2}\left[t^{4}\right]_{0}^{2}$ = 24 J
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