Question

A particle moves so that its position vector varies with time as `vec(r )= A cos omegathat(i)+A sin omega t hai(j)`. The initial velocity of the particel the particle is
A. `A omega hat(i)`
B. `A omega hat(j)`
C. `A omega(hat(i)+hat(j))`
D. `A omega (hat(i)-hat(j))`

Answer 1

Correct Answer - B
Substituting `vec(r )=(A cos omega t hat(i)+A sin omega t hat(j))`
in `vec(v)= (dvec(r ))/(dt)` we have `vec(v) = A(d)/(dt)(cos omega t)hat(i)+A(d)/(dt)(sin omega t)hat(j)`
`= - A omega sin omega t hat(i)+A omega cos omega t hat(j)`
At `t = 0 , v= - A omega sin 0 hat(i)+A omega cos 0hat(j)= A omegahat(j)`