A particle is subject to a force F_x=F_0 e^(-ct), where F_0 and c are positive constants, and starts moving from rest at x=0 and t

Find the position of the particle x as a function of time t.
Find the velocity of the particle x ̇ as a function of time t.
Describe (in words and mathematically) the motion of the particle after a long time.
Define a conservative force. Is the force in the problem above conservative?

Given that the velocity of a particle in rectilinear motion varies with the displacement x as:
x ̇=cx^(-4)
where c is a positive constant. Find the force acting on the particle as a function of x.