A particle is moving with a constant speed V in a circle. What is the magnitude of average velocity after onefourth rotation?

Question

A particle is moving with a constant speed V in a circle. What is the magnitude of average velocity after onefourth rotation? (A) (π V /√2) (B) (√2 V /π) (C) (2 √2 V /π) (D) (π R/2 V)

Tardigrade Admin · Accepted Answer

Let R be the radius of the circle Displacement of particle = r <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/25034d963c766fb6605b4cd82fb0ddea-.png" /> Average velocity =( text displacement / text time ) Time =(π R /2 V )( V = velocity ) r =√ R 2+ R 2=√2 R Average velocity =(√2 R /(π R )2 V )=(2 √2 V /π)

Q. A particle is moving with a constant speed $V$ in a circle. What is the magnitude of average velocity after onefourth rotation?

$\frac{πV}{2}$

$\frac{2 V}{π}$

$\frac{2 2 V}{π}$

$\frac{π R}{2 V}$

Let $R$ be the radius of the circle Displacement of particle $= r$

Average velocity $= \frac{displacement}{time}$
Time $= \frac{π R}{2 V} (V =$ velocity $)$
$r = R^{2} + R^{2} = 2 R$
Average velocity $= \frac{2 R}{\frac{π R}{2 V}} = \frac{2 2 V}{π}$

Q. A particle is moving with a constant speed V in a circle. What is the magnitude of average velocity after onefourth rotation?

2​πV​

π2​V​

π22​V​

2VπR​