A particle of mass `m` moves due to the force `F=-alpha m r, ` where `alpha` is a positve constant ,` r` is the radius vector of the particle relative to the origin of coordinates. Find the trajectory of its motion if at the initial moment `r=r_(0)i` and the velocity `v=upsilon_(0)j`, whee `i` and `j` are the unit vectors of the `x` and `y` axes.

A particle of mass m moves in a circular orbit under the central potential field, U(r)==-C/r, where C is a positive constant. The correct radius -velocity graph of the particle's motion is.

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 radius vector of point A relative to the origin varies with time t as vec r = at hat i - bt^2 hat j where a and b are constant. The equation of point's trajectory is.

A radius vector of point A relative to the origin varies with time t as vec r = at hat i - bt^2 hat j where a and b are constant. The equation of point's trajectory is.

A force F=Ai+Bj is applied to a point whose radius vector relative to the origin of coordinates O is equal to r=ai+bj , where a, b, A, B are constants, and i,j are the unit vectors of the x and y axes. Find the moment N and the arm l of the force F relative to the point O.

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 of mass 0.2 kg is moving with linear velocity (i-j+2k) . If the radius vector r=4i+j-k , the angular momentum of the particle is

A particle of mass 0.2 kg is moving with linear velocity (i-j+2k) . If the radius vector r=4i+j-k , the angular momentum of the particle is

A force F_1=Aj is applied to a point whose radius vector r_1=ai , while a force F_2=Bi is applied to the point whose radius vector r_2=bj . Both radius vectors are determined relative to the origin of coordinates O, i and j are the unit vectors of the x and y axes, a, b, A, B are constants. Find the arm l of the resultant force relative to the point O.