A particle is moving in a plane with a velocity given by, `vecu=u_(0)hati+(omegacosomegat) hatj,` are unit vectors along x and y-axes respectively. If the particle is at the origin an `t=0,` then its distance from the origin at time`t=3pi//2omega` will be

A particle is moving in a plane with velocity given by vec(u)=u_(0)hat(i)+(aomega cos omegat)hat(j) , where hat(i) and hat(j) are unit vectors along x and y axes respectively. If particle is at the origin at t=0 . Calculate the trajectory of the particle :-

A particle is moving in a plane with velocity vec(v) = u_(0)hat(i) + k omega cos omega t hat(j) . If the particle is at origin at t = 0 , (a) determine the trajectory of the particle. (b) Find its distance from the origin at t = 3pi//2 omega .

A particle in moving in a straight line such that its velocity is given by v=12t-3t^(2) , where v is in m//s and t is in seconds. If at =0, the particle is at the origin, find the velocity at t=3 s .

A particle projected from origin moves in x-y plane with a velocity vecv=3hati+6xhatj , where hati" and "hatj are the unit vectors along x and y axis. Find the equation of path followed by the particle :-

An ant is moving in x-y plane with its position vector vecs=2t^2hati+5hatj then, velocity vector of it at t = 1 sec is:

A particle moves in xy plane with its position vector changing with time (t) as vec(r) = (sin t) hati + (cos t) hatj ( in meter) Find the tangential acceleration of the particle as a function of time. Describe the path of the particle.

A particle moves in plane with acceleration veca = 2hati+2hatj . If vecv=3hati+6hatj , then final velocity of particle at time t=2s is

The angular velocity of a particle is vec(w) = 4hati + hatj - 2hatk about the origin. If the position vector of the particle is 2hati + 3hatj - 3hatk , then its linear velocity is