Problem 1(on kinematics)

1.A particle is going in a velocity `\vec v=a\hati+bx^2\hatj` where  `a` and `b` is constant and at `t=0` the particle was at origin then find the following

a) trajectory of the particle

b) radius of the curvature

2.A particle moves in one direction along a given trajectory with a tangential acceleration `a_{\tau}=a\tau` where `a` is a constant vector coinciding in direction with the `x` axis and `\tau` is a unit vector coinciding in direction with the velocity vector at a given point. Find how the velocity of the particle depends on `x` provided that it's velocity in negligible at the point `x=0`.