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 move in x-y plane such that its position vector varies with time as vec r=(2 sin 3t)hat j+2 (1-cos 3 t) hat j . Find the equation of the trajectory of the particle.

A particle move in x-y plane such that its position vector varies with time as vec r=(2 sin 3t)hat j+2 (1-cos 3 t) hat j . Find the equation of the trajectory of the particle.

A particle move so that its position verctor varies with time as vec r=A cos omega t hat i + A sin omega t hat j . Find the a. initial velocity of the particle, b. angle between the position vector and velocity of the particle at any time, and c. speed at any instant.

A particle move so that its position verctor varies with time as vec r=A cos omega t hat i + A sin omega t hat j . Find the a. initial velocity of the particle, b. angle between the position vector and velocity of the particle at any time, and c. speed at any instant.

A particle moves so that its position vector varies with time as vec(r )= A cos omegathat(i)+A sin omega t hai(j) . The initial velocity of the particel the particle is

A particle moves on the xy-pane such that its position vector is given by vec(r)=3t^(2) hati-t^(3) hatj . The equation of trajectory of the particle is given by

A particle of mass m moves in xy plane such that its position vector, as a function of time, is given by vec(r) =b(kt-sinkt)hati+b(kt+cos kt) hatj . where b and k are positive constants. (a) Find the time t_0 in the interval o le t le (pi)/k when the resultant force acting on the particle has zero power. (b) Find the work done by the resultant force acting on the particle in the interval t_(o) le t le (pi)/4

The position vector of a particle is given by vecr=(2 sin 2t)hati+(3+ cos 2t)hatj+(8t)hatk . Determine its velocity and acceleration at t=pi//3 .