A particle of mass moves along the -axis such that its velocity at any instant is given by

PHYSICS · Multi-part · CBSE · Physics · Force and Laws of Motion · Force and Laws of Motion

Problem

A particle of mass

2.0\,\text{kg}

moves along the

x

-axis such that its velocity at any instant is given by

v(t)=4t-t^{2}

, where

v

is in

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

and

t

in seconds (

0\le t\le4

). (i) Derive an expression for the instantaneous force acting on the particle as a function of time. (ii) Determine the instant between

t=0

and

t=4\,\text{s}

when this force becomes zero. (iii) Calculate the impulse imparted to the particle during the interval from

t=0

t=4\,\text{s}