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Question

# A body is in motion along the positive x - axis, according to the relation x=asin2ωt. Then, the variation of its kinetic energy K with time t may be represented by

A
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B
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C
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D
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Solution

## The correct option is D The instantaneous velocity of the body is v=dxdt =ddt(a sin2ωt) =2aω sin ωt cos ωt =aω sin 2 ωt Let the mass of the body is m. The expression for the kinetic energy of the body is K=12mv2 Substitute the known values. K=12m(aωsin 2ωt)2 =12ma2ω2sin22ωt......(1) K=12ma2ω2(1−cos4ωt)2 The time period of the expression of kinetic energy is 2π4ω=π2ω The maxima of the equation of kinetic energy occurs at π4ω. The kinetic energy will be zero at t=0. Hence option d is satisfying the equation of kinetic energy.

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