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

Question

Power applied to a particle varies with time as P=(.3t2-2t+1.) watt, where t is in second. The change in its kinetic energy between t=2 s and t=4 s is (A) 32J (B) 46J (C) 61J (D) 100J

Tardigrade Admin · Accepted Answer

P=3t2-2t+1=(d E/d t) ∴ dE=(.3t2-2t+1.)dt E= displaystyle ∫ t = 2 st = 4 s (. 3 t2 - 2 t + 1 .) d t =[(3 t3/3) - (2 t2/2) + t]t = 2 st = 4 s =[.(43 - 23)-(42 - 22)+(.4-2.)]. E=56-12+2=46 J

Q. 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 $t = 2 s$ and $t = 4 s$ is

$32 J$

$46 J$

$61 J$

$100 J$

$P = 3 t^{2} - 2 t + 1 = \frac{d E}{d t}$
$∴ d E = (3 t^{2} - 2 t + 1) d t$
$E = \int_{t = 2 s}^{t = 4 s} (3 t^{2} - 2 t + 1) d t$
$= [\frac{3 t ^{3}}{3} - \frac{2 t ^{2}}{2} + t]_{t = 2 s}^{t = 4 s}$
$= [(4^{3} - 2^{3}) - (4^{2} - 2^{2}) + (4 - 2)]$
$E = 56 - 12 + 2 = 46 J$

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

32J

46J

61J

100J