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## Homework Statement

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?

## Homework Equations

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.

Thanks