Equations of motion of a test particle in a time-dependent force field?

Question

Consider a test particle of mass m that is free to move in a 2-dimensional plane. A time-dependent force pulls the particle towards the origin. The magnitude of the force is F*t. What are the equations of motion for the test particle?

Answer 1

Dynamic equation:
ma = F(t) = Fo t

Solution:
m dv/dt = Fo t
∫m dv = ∫Fo t dt
v = Fo/m t²/2 + Vo

dr/dt = Fo/m t²/2 + Vo
∫m dr = ∫[Fo/m t²/2 + Vo] dt

Answer:
r(t) = Fo/m t³/6 + Vo t + Ro

Answer 2

A force which is moving as a function of time behaves as a wave. The force oscillates as it travels thru a medium.
As far as a particle is concerned it cannot move unless power is applied top cause it to move.
As power is applied to the mass particle a force is born. It will then move with the power that it was given to move. As the test particle is moving it will increase in speed and at the same time the moving force amplitude will decrease till the particle has reached its final velocity at the end of the period of its oscillation.
The equation to cause the particle motion is Power=Force x velocity that the force move for one period of oscillation.
[ P=F(t) x V]

If a force moves ,it is of course depending on time for its motion.
Forces are always the result of a push(a disturbense.)
A force moving in a straight line is equivalent to a force moving in a circular path on a two dimensional plane.