These are the same problems you posted under "friction question".
1. a block with mass m slides on a horizontal surface. the block is intially at x=0 with velocity v0.
the frictional force that the block experience is proportional to v^(3/2)
such that
F(v)=-kv^(3/2)
for positive constant K. what is the max distance that the block travel?
2. a particle of mass m is under the influences of a force F(x) that attracts the particle according to
F(x) = -kx^(-2)
where x is the distance from a fixed origin at x=0 and k is a positive constant
if the particle is released from the rest at x=d, how long does it take to reach the origin?