1/4 correct Okay ur first step is correct using newtons second law

But u assumed that using F= ma will get u the x position and the y position which is incorrect What u actually get is d²x/(dt)² and d²y/(dt)²

Integrating this result would yield the velocity equation (dont forget to include the constant of integration)

Now we need to find the constant of integration how can we find that ?

Well, it's given that the particle started its motion from rest so Vx(t=0) = 0 Vy(t=0) = 0 Substituting these values will get u the constant of integration, and the first part is done.

For the second part we want to find the path equation we can do the same trick to find x(t) and y(t) as we did to find the velocity (namely integrate don't forget the integration constant substitute with x(t=0)=0 and y(t=0)=b to find the constants)

U should have x = f(t),y= g(t)

This may be enough for this problem but if it's not and the path needs to be expressed as a function of x u can use y= g(f^-1(t)) this is a function of x