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:

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)=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 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 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 of a particle is given by vec r =3.0 t hat I + 2.0 t^(2) hat j+ 5.0 hat k wher (t) in seconds and the coefficients have the proper units . Find the velocity and acceleration of the particle in magnitude and direction at time t=3.0 s

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 :

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 :