Power applied to a particle varies with time as $P = (3 t^{2} - 2 t + 1) W$ , where $t$ is in second. Find the change in its kinetic energy as time changes from $t = 2 s$ to $t = 4 s$ .

32 J

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46 J

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61 J

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102 J

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Solution

The correct option is B $46 J$
By definition of power $P = \frac{d W}{d t}$
From work energy theorem
$Δ K E = W = \int_{2}^{4} Pdt = \int_{2}^{4} (3 t^{2} - 2 t + 1) d t$
$Δ K E = [t^{3} - t^{2} + t]_{2}^{4}$
$Δ K E = 46 J$

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Similar questions

P = (3 t^{2} - 2 t + 1) W

t

t = 2 s

t = 4 s

P = (3 t^{2} - 2 t + 1)

P = (3 t^{2} - 2 t + 1) w a t t

t = 2 s

t = 4 s

P = [3 t^{2} - 2 t + 1]

P = (3 t^{2} - 2 t + 1)

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