A particle moves in the plane `xy` with velocity `v=ai+bxj`, where i and j are the unit vectors of the x and y axes, and a and b are constants. At the initial moment of time the particle was located at the point `x=y=0`. Find:
(a) the equation of the particle's trajectory `y(x)`,
(b) the curvature radius of trajectory as a function of x.

A particle of mass m moves in pane xy due to the force varying with velocity as F=a(dot(y)-dot(x)j) , where a is a positve constant, i and j are the unit vectors of the x and y axes. At the initial moment t=0 the particle was located at the point x=y=0 and possessed a velocity v_(0) directed along the unit vector j . Find the law of motino x(t), y(t) of the particle, and also the equation of its trajectory.

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 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 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 :-

The velocity of a particle moving in the x direction varies as V = alpha sqrt(x) where alpha is a constant. Assuming that at the moment t = 0 the particle was located at the point x = 0 . Find the acceleration.

A particle of mass m moves in the xy-plane with velocity of vec v = v_x hat i+ v_y hat j . When its position vector is vec r = x vec i + y vec j , the angular momentum of the particle about the origin 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.