Question

a particle is moving on a circular path with constant speed v what is the change in velocity after it has described an angle of 60°

Answer 1

the linear velocity vector is perpendicular to the radius and has a magnitude of v always.

let the initial velocity vector be along +ve x axis.. so   v1 = v i.   When the body has traveled so that it describes an angle of 60° at the center of circle, the velocity vector = v2 will also turn by 60 deg. towards  +ve y axis.

$\vec{\Delta v}=\vec{v_2}-\vec{v_1}=(v*Cos60^0\vec{i}+v*Sin60^0\vec{j})-v*\vec{i}\\\\.\ \ \ =\frac{v}{2}(-\vec{i}+\sqrt3\ \vec{j})\\\\\theta=tan^{-1}(-\sqrt3)=120^0\ wrt\ +ve\ x-axis.\\\\magnitude=v$