Find the velocity v and position r as functions of t for a particle of mass m which starts from rest at x=0 at time t=0 and subject to the following forces:
F=Fo
F=Fo +bti
F=Fo coswt
F=kt^2
In each case, F/m is the acceleration.
Integrate that twice to get x vs time. You will need the fact that x=0 and V=0 at t=0.
I have no idea what the "i" is in the second equation. It cannot be the square root of -1.