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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(1cos4ωt)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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