Question

a particle is moving in a circular path of radius r with constant speed u calculate the magnitude and change in velocity 1) when it completes half rotation and 2) 1/4r rotation​

Answer 1

Let the velocity at point P

$\large\rm { \vec{v}_{1} = v \hat{i}}$

So, the velocity at Point Q

$\large\rm { \vec{v}_{2} = v \ \cos 40^{\circ} \ \hat{i} - v \ \sin 40^{\circ} \hat{j}}$

change in velocity:

$\large\rm { \Delta v = (v \ \cos 40^{\circ} \ \hat{i} - v \ \sin 40^{\circ} \hat{j}) - v \hat{i}}$

Magnitude of change in Velocity

$\large\rm { | \Delta v| = \sqrt { ( v \ \cos \ 40^{\circ} - v)^{2} + (- v \ \sin 40^{\circ})^{2}}}$

on solving we get

$\large\rm { | \Delta v| = 2v \ \sin 20^{\circ}}$

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