The velocity of a motorcycle of mass moving along a straight road is given by

PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power

Problem

The velocity of a motorcycle of mass

250\,\text{kg}

moving along a straight road is given by

v=5 t^{1/2}

, where

v

is in

\text{m\,s}^{-1}

and

t

in seconds (

t\ge 0

). The motion starts from rest at

t=0

. (i) Derive an expression for the instantaneous power developed by the motorcycle’s engine as a function of time. (ii) Calculate the power at

t=4\,\text{s}

and at

t=9\,\text{s}

. (iii) Find the ratio of the two powers obtained in part (ii).