A particle moves in the plane xy with velocity `vec V=ahat i+bxhat j` where i and j are the unit vectors along x and y axis,and a and b are constant.At the initial moment of time the particle was located at the point x=y=0.The equation of the particle trajectory is

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 :-

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 with velocity vecv = k( y hat(i) + x hat(j)) , where k is a constant . The genergal equation for its path is

A particle is moving with velocity vecv = k( y hat(i) + x hat(j)) , where k is a constant . The genergal equation for its path is

A particle is moving with velocity vecv = k( y hat(i) + x hat(j)) , where k is a constant . The genergal equation for its path is

The angle which the vector vec(A)=2hat(i)+3hat(j) makes with the y-axis, where hat(i) and hat(j) are unit vectors along x- and y-axis, respectively, is

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 is moving with constant speed v along x - axis in positive direction. Find the angular velocity of the particle about the point (0, b), when position of the particle is (a, 0).

The velocity of a particle moving in the positive direction of the x axis varies as v=alphasqrtx , where alpha is a positive constant. Assuming that at the moment t=0 the particle was located at the point x=0 , find: (a) the time dependence of the velocity and the acceleration of the particle, (b) the mean velocity of the particle averaged over the time that the particle takes to cover the first s metres of the path.

A particle moves in the XY-plane according to the law x = kt, y = kt (1- alphat) , where k and alpha are positive constants and t is time. The trajectory of the particle is