Power supplied 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 between time t = 2 s to t = 4 s is-

46 J

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52 J

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92 J

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104 J

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Solution

The correct option is A 46 J
Energy supplied to the system = change in energy of system.
$Δ K . E . = \int P d t$
$= \int_{2}^{4} (3 t^{2} - 2 t + 1) d t$
$= [t^{3} - t^{2} + t]_{2}^{4}$
$Δ K . E = (4)^{3} - (4)^{2} + 4 - (2)^{3} + (2)^{2} - 2$
$= 64 - 16 + 4 - 8 + 4 - 2$
$= 46 J$

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Q. Power applied to a particle varies with time as

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

The correct option is A 46 JEnergy supplied to the system = change in energy of system. ΔK.E.=∫Pdt =∫42(3t2−2t+1)dt =[t3−t2+t]42 ΔK.E=(4)3−(4)2+4−(2)3+(2)2−2 =64−16+4−8+4−2 =46 J

Power supplied 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 between time t = 2 s to t = 4 s is-

The correct option is A 46 J
Energy supplied to the system = change in energy of system.
$Δ K . E . = \int P d t$
$= \int_{2}^{4} (3 t^{2} - 2 t + 1) d t$
$= [t^{3} - t^{2} + t]_{2}^{4}$
$Δ K . E = (4)^{3} - (4)^{2} + 4 - (2)^{3} + (2)^{2} - 2$
$= 64 - 16 + 4 - 8 + 4 - 2$
$= 46 J$