Power applied to a particle varies with time as $P = [3 t^{2} - 2 t + 1]$ watts, where t is time in seconds. Then the change in kinetic energy of particle between time t = 2 s to t = 4 s is (in Joule) –

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Solution

$w = Δ K E$
$\frac{d w}{d t} = P$
$\int d w = \int P d t$
$w = \int_{2}^{4} (3 t^{2} - 2 t + 1) d t$
${[\frac{3 t^{3}}{3} - \frac{2 t^{2}}{2} + t]}_{2}^{4}$
$= (t^{3} - t^{2} + t)_{2}^{4} = 46$
$w = Δ K . E = 46 J$

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Power applied to a particle varies with time as P=[3t2−2t+1] watts, where t is time in seconds. Then the change in kinetic energy of particle between time t = 2 s to t = 4 s is (in Joule) –

w=ΔKE dwdt=P ∫dw=∫Pdt w=∫42(3t2−2t+1)dt [3t33−2t22+t]42 =(t3−t2+t)42=46 w=ΔK.E=46 J

Power applied to a particle varies with time as $P = [3 t^{2} - 2 t + 1]$ watts, where t is time in seconds. Then the change in kinetic energy of particle between time t = 2 s to t = 4 s is (in Joule) –

$w = Δ K E$
$\frac{d w}{d t} = P$
$\int d w = \int P d t$
$w = \int_{2}^{4} (3 t^{2} - 2 t + 1) d t$
${[\frac{3 t^{3}}{3} - \frac{2 t^{2}}{2} + t]}_{2}^{4}$
$= (t^{3} - t^{2} + t)_{2}^{4} = 46$
$w = Δ K . E = 46 J$