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

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 C 46 J
Energy supplied to the system = change in energy of system.
Since only energy of system is kinetic,
$\int P d t = Δ K E = \int_{2}^{4} 3 t^{2} - 2 t + 1 d t = [t^{3} - t^{2} + t]_{2}^{4}$
$Δ K E = 4^{3} - 4^{2} + 4 - 2^{3} + 2^{2} - 2 = 46 J$

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Power applied to a particle varies with time as P=(3t2−2t+1) watt, where t is in second. Find the change in its kinetic energy between time t=2s and t=4s

The correct option is C 46 JEnergy supplied to the system = change in energy of system.Since only energy of system is kinetic,∫Pdt=ΔKE=∫423t2−2t+1dt=[t3−t2+t]42ΔKE=43−42+4−23+22−2=46J

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

The correct option is C 46 J
Energy supplied to the system = change in energy of system.
Since only energy of system is kinetic,
$\int P d t = Δ K E = \int_{2}^{4} 3 t^{2} - 2 t + 1 d t = [t^{3} - t^{2} + t]_{2}^{4}$
$Δ K E = 4^{3} - 4^{2} + 4 - 2^{3} + 2^{2} - 2 = 46 J$