A particle moves in the – plane such that its velocity vector at time is given by

PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

A particle moves in the

x

–

y

plane such that its velocity vector at time

t

is given by

\mathbf v(t)=\bigl(A\cos \omega t\,\hat{\imath}+A\sin \omega t\,\hat{\jmath}\bigr)

, where

A

and

\omega

are positive constants. (a) Determine an expression for the speed

s(t)

of the particle. (b) Show that the speed remains constant with time and state its value. (c) If

A=2.5\,\text{m\,s}^{-1}

and

\omega=\pi\,\text{s}^{-1}

, calculate the speed at

t=0.75\,\text{s}

. Comment on your result with reference to part (b).