If the position vector of a particle is given by `vec r =(94 cos 2t) hat i + (4 sin 2t) hat j + (6t) hat km`, calculate its acceleration at `t=pi//4 second `.

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 ) = (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)

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.

The position vector of a particle is determined by the expression vec r = 3t^2 hat i+ 4t^2 hat j + 7 hat k . The displacement traversed in first 10 seconds 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 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 time dependence of the position of a particle of mass m = 2 is given by vec(r) (t) = 2t hat(i) - 3 t^(2) hat(j) Its angular momentum, with respect to the origin, at time t = 2 is :

The position vector of a moving particle at 't' sec is given by vec r=3hat i+4t^(2)hat j-t^(3)hat k .Its displacement during an interval of t =1 s to 3 sec is (A) hat j-hat k (B) 3hat i+4hat j-hat k (C) 9hat i+36hat j-27hat k (D) 32hat j-26hat k

The position vector of a particle is given by vec(r)=1.2 t hat(i)+0.9 t^(2) hat(j)-0.6(t^(3)-1)hat(k) where t is the time in seconds from the start of motion and where vec(r) is expressed in meters. For the condition when t=4 second, determine the power (P=vec(F).vec(v)) in watts produced by the force vec(F)=(60hat(i)-25hat(j)-40hat(k)) N which is acting on the particle.

The position of a particle is given by vec r= 3.0 t hat I - 2 2- 0 t^@ hat j + 4.0 hat k m , wher 9t) in seconds and the coefficits have the proper units for vec r to be in metres. (a) Fing the vec v and ve a of the particle ? (b) What is the magnitude and direction fo velocity of the particle at t= 2 s ?