If the position vector of a particle is given by `vec(r ) = (cos 2t) hat(i) + (sin 2 t) hat(j) + 6 t hat(k) m`. Calculate magnitude of its acceleration (in `m//s^(2)` ) at `t = (pi)/(4)`

If the position vector of a particle is given by vec r =(4 cos 2t) hat j + (6t) hat k m , calculate its acceleration at t=pi//4 second .

If the position vector of a particle is given by vec r= 5t^(2)hat i +7t hat j +4 hat k , then its velocity lies in:

The position of a particle is given by vec(r) = 3that(i) - 4t^(2)hat(j) + 5hat(k). Then the magnitude of the velocity of the particle at t = 2 s is

The position vector of a particle changes with time according to the relation vec(r ) (t) = 15 t^(2) hat(i) + (4 - 20 t^(2)) hat(j) What is the magnitude of the acceleration at t = 1?

Position vector of a particle moving in space is given by : vec(r)=3sin t hat i+3 cos t hatj+4 t hatk Distance travelled by the particle in 2s is :

Position vector of a particle moving in space is given by : vec(r)=3sin t hat i+3 cos t hatj+4 t hatk Distance travelled by the particle in 2s is :

The position vector of a particle is given by vec(r ) = k cos omega hat(i) + k sin omega hat(j) = x hat(i) + yhat(j) , where k and omega are constants and t time. Find the angle between the position vector and the velocity vector. Also determine the trajectory of the particle.