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Power applied to a particle varies with time as $P = (3 t^{2} - 2 t + 1) watt$ , where t is in second. The change in its kinetic energy between time t = 2 sec. and t = 4 sec. is

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32 J

46 J

61 J

102 J

answer is B.

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Detailed Solution

$W = \int_{2}^{4} Pdt = {[t^{3}]}_{2}^{4} - {[t^{2}]}_{2}^{4} + {[t]}_{2}^{4}$
$∆ K = W = [64 - 8] - [16 - 4] + [4 - 2] = 56 - 12 + 2 = 46 J$

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