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

1. 12 J
2. 24 J
3. 36 J
4. 48 J

Correct answer: 12 J

Solution

The displacement is given as s = (1/3)t². Differentiating with respect to time, velocity v = ds/dt = (2/3)t. At t = 2 s, v = (2/3)(2) = 4/3 m/s. The acceleration a = dv/dt = 2/3 m/s². Force F = ma = 3 × (2/3) = 2 N. Work done W = F × s = 2 × (1/3)(2²) = 12 J.

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