A particle starts moves in the plane xy with constant acceleration w directed along the negative y direction. The equation of the motion of the particle has the form y = ax - bx^2, where a and b are positive constants. Find the velocity of the particle at the origin of the co-ordinates. The problem maker has completed the question without giving us from where did the particle start. So we even do not know the velocity of the particle along the y direction, thus e cannot relate it along the X-axis. So I think that the problem must be with the particle moving with constant velocity w along the negative Y-axis. But anyway we have not been given when does the object pass through the origin. Thus we cannot make a time equation to solve the question. Anyway the slope of the XY graph as it reaches the origin is a. therefore the velocity of the particle along Y-axis is -a times the velocity of the particle along the X-axis. Therefore if the velocity of the particle along the X-axis is v, then v = -aw. Therefore the magnitude of velocity is (v^2 + w^2)^1/2 which we finally get as w(1 + a^2)^1/2. I don't know whether my work is correct in this case. Also I want to know whether the problem can be solved with respect to a, b and w when w is the constant acceleration of the particle along the negative Y- direction.