Work, Power and EnergyHard

Question

A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the x-axis. Its kinetic energy K changes with time as dK/dt = γt, where γ is a positive constant of appropriate dimensions. Which of the following statements is (are) true ?

Options

A.

The force applied on the particle is constant

B.

The speed of the particle is proportional to time

C.

The distance of the particle from the origin increses linerarly with time

D.

The force is conservative

Solution

dkdt=γt  as k=12mv2dkdt=mvdvdt=γt
movvdv=γottdt
mv22=γt22
v=γmt     .............(i)    
a=dvdt=γm=constant
since F = ma
F=mγm=γm=constant

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