Question

the position of the particle is vector r=(a costheta t) + (sin theta t)

Answer 1

If a position vector is given then you can find it's velocity but simply differentiating it with respect to time. You have time (t) in the position vector.

Theta=© ;

r= a Cos(©*t) i + a Sin(©*t) j ;

(dr/dt)= V (velocity);

V= a [ {-Sin(©*t) * ©} + {Cos(©*t) * ©} ] ;

V = a*© {Cos(©*t) — Sin(©*t)} ;

Velocity will be