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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 meters and t is in seconds. The work done by all the forces acting on the body during the time interval t = 2s 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

v = $\frac{dS}{dt}$ = 2t+2

From work energy theorem;

$W_{n e t} =$ $∆ K . E .$ = $K_{f} - K_{t}$

= $\frac{1}{2} m$ ( ${v_{f}}^{2}$ - ${v^{2}}_{i}$ )

= $\frac{1}{2} \times 2 {[2 \times 4 + 2]}^{2}$ -(2 $\times$ 2+2 $)^{2}$ ] = 64 J

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