A particle moves in a plane such that its coordinates changes with time as `x = at` and `y = bt`, where a and b are constants. Find the position vector of the particle and its direction at any time t.

A particle moves in the x-y plane such that its coordinates are given x = 10sqrt(3) t, y = 10t - t^(2) and t is time, find the initial velocity of the particle.

A particle is moving in x-y plane with its x and y co-ordinates varying with time as, x=2t and y=10t-16t^2. Find trajectory of the particle.

A particle is moving in x-y plane with its x and y co-ordinates varying with time as, x=2t and y=10t-16t^2. Find trajectory of the particle.

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 so that its coordinates vary with time as x= alpha sin omegat,y=alpha cos omegat and z=bt^(2) . Find the initial: (a) position (b) velocity (c) acceleration of the particle.

A particle moves in a circular path of radius R with an angualr velocity omega=a-bt , where a and b are positive constants and t is time. The magnitude of the acceleration of the particle after time (2a)/(b) is

A particle moves in a circular path of radius R with an angualr velocity omega=a-bt , where a and b are positive constants and t is time. The magnitude of the acceleration of the particle after time (2a)/(b) is

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.

For a particle moving in the x-y plane, the x and y coordinates are changing as x=a sin omega t and y = a ( 1-cos omega t ) , where 'a' and omega constants. Then, what can be inferred for the trajectory of the particle ?