Question

Under the action of a force, a 2 kg body moves such that its position x as function of time is given by x = 2t^(4)+ 5, where x is in metres and t is in seconds. The incase in kinetic energy one second after the start of nation is (A) 8J (B) 16J (C) 32J (D) 64J

Answer 1

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16 J

Explaination :-

Position of the body varies as x= $\frac{ {t}^{3} }{3}$

Thus the acceleration of the body at any instant= $\frac{ {d}^{2}x }{d {t}^{2} } = 2t$

Force any on body at any instant = ma = 2mt

Thus work done on body in moving the object by a distance dx = F.dx = 2mtdx =$2mt( {t}^{2} dt)$

Thus total work done in 2s= $2s {∫}^{2} _{0}2m {t}^{2} dt = 16 \: J$

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