Question

A particle is moving along a circle such that its
position vector with respect to origin is
r = 2r° (sinwti^ + coswtj^), where r° and w are
constant. The motion is with
(1) Constant speed
12) Constant velocity
43) Constant acceleration
14) Constant momentum​

Answer 1

answer : option (1) constant speed

explanation : A particle moves along a circle such that its position vector with respect to origin is $r=2r_0(sin\omega t\hat{i}+cos\omega t\hat{j})$

where r and ω are constants.

differentiating with respect to time,

dr/dt = $2r_0$[d(sinωt)/dt i + d(cosωt)/dt j ]

= $2r_0$(-ωcosωt i + ωsinωt j)

= $2r_0\omega$(-cosωt i + sinωt j)

so, velocity of particle is v = dr/dt = $2r_0\omega$(-cosωt i + sinωt j)

now, speed of particle = |v|

= $2r_0\omega\sqrt{sin^2(\omega t)+cos^2(\omega t)}$

= $2r_0\omega$ (constant )

hence, it is clear that speed of particle is constant.

hence, option (1) is correct choice

Answer 2

Answer:

constant speed becoz in circular motion the direction of tangential velocity and tengential acceleration keeps changing hence it's never constant