__Question 6.9__:*t*is proportional to

(i) t

^{1/2}(ii) t (iii) t

^{3/2}(iv) t

^{2}

^{}

__Solution__:Mass of the body =

*m*

Acceleration of the body =

*a*

Using Newton’s second law of motion, the force experienced by the body is given by the equation:

*F*=

*ma*

Both

*m*and

*a*are constants. Hence, force

*F*will also be a constant.

*F*=

*ma*= Constant … (

*i*)

For velocity

*v*, acceleration is given as,

a = dv / dt = Constant

dv = Constant X dt

v = αt ...(ii)

Where α is another constant

v ∝ t ...(iii)

Power is given by the relation:

*P = F*.

*v*

Using equations (

*i*) and (

*iii*), we have:

*P*∝

*t*

Hence, power is directly proportional to time.

Option (ii) is the answer

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