4. A particle of mass m is experiences a Force that attracts the particle following
F(x) = -k*x^-2
(an inverse square relationship) where x is the distance from an origin at x = 0 and k is a
positive constant. If the particle is released from rest at x = d, how long does it take to reach the origin?
F = ma = m(dv/dt)
The Attempt at a Solution
Equating newton's second and the Force equations yields -k*x^-2 = m(dv/dx)(v).
After seperating the variables and integrating once, I got V = sqrt(2k/m)*sqrt((1/x)-(1/d)).
My boundary condition was that at x = d, v =0 for the integration. Setting V = dx/dt and trying to solve for x(t) is unfathomable, so I'm not sure how to continue here, or if I have been taking the wrong approach. I've double checked my math as well, so I don't believe the error is there, but I could always be wrong.