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The displacement of a body of mass 2 kg varies with time 't' as $S = t^{2} + 2t$ , where S is in metres and 't'is in seconds. The work done by all the forces acting on the body during the time interval t = 2 s to t = 4 s is

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36 J

64 J

100 J

120 J

answer is B.

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Detailed Solution

S = t^{2} + 2 t

$\frac{ds}{dt} = 2 t + 2$

$v = 2 t + 2$

$v_{t = 2} = 2 \times 2 + 2 = 4 + 2 = 6 m / s$

$v_{t = 4} = 2 \times 4 + 2 = 8 + 2 = 10 m / s$

$W = \frac{1}{2} m (v^{2} - u^{2})$

$W = \frac{1}{2} \times 2 \times (100 - 36)$

$W = 64 J$

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