A body of mass 3 kg is under a constant force which causes a displacement s in metres in it, given by the relation s = 1/3 t2, where t is in seconds. Work done by the force in 2 seconds is (a) 19/5 J (b) 5/19 J (c) 3/8 J (d) 8/3 J

Answer: (d). s = t²/3 ⇒ v = ds/dt = 2t/3; at t = 0, v = 0. At t = 2 s: v = 4/3 m/s W = Δ K = 1/2(3)(4/3)² = 8/3 J So the answer is (d).

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Q26NEET 2006 · AIPMTEasy

Work-Energy Theorem

A body of mass 3 kg is under a constant force which causes a displacement s in metres in it, given by the relation s = $\frac{1}{3}$ t2, where t is in seconds. Work done by the force in 2 seconds is

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Answer: (d)

$s = \frac{t^2}{3} \Rightarrow v = \frac{ds}{dt} = \frac{2t}{3}$ ; at $t = 0$ , $v = 0$ .
At $t = 2$ s: $v = \frac{4}{3}\text{ m/s}$
$W = \Delta K = \frac{1}{2}(3)\left(\frac{4}{3}\right)^2 = \frac{8}{3}\text{ J}$
So the answer is (d).

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