A particle of mass m is released from rest at a distance b from a fixed origin of force that attracts the particle according to the inverse square law:(adsbygoogle = window.adsbygoogle || []).push({});

F = -kx^-2

Show that the time required for the particle to reach the origin is:

[pi](mb^3/8k)^1/2

I have no idea where the pi came from.

This is what I've done.

F=dp/dt

dp/dt=mdv/dt

dv/dt=d^2x/dt^2

m*d^2x/dt^2=m*dv/dt

m*d^2x/dt^2=-k/x^2

m*x^2*d^2x=-k*dt^2

m[inte][inte]x^2dxdx=-k[inte][inte]dtdt

After solving the double integrals and pluging in the constants I get.

t = sqrt[-1/(6k)*m(16b^4)]

I'm going to be really embarrased if my calculus is wrong.

So am I doing wrong. I still have no idea where a pi comes from!

Thanks

Frank

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