^{2}per unit mass towards the origin. Find the time taken to reach the origin if the particle starts at rest 4 units from the origin.

I have been able to arrive at an equation:

a(x) = 2/x

^{2}(as force per unit mass, I am assuming mass to be 1 unit)

a(x) = dv/dt = dv/dx . dx/dt = v dv/dx (chain rule)

Hence, v dv = (2/x

^{2}) dx

v

^{2}/2 = (-2/x

^{2}) + c

v

^{2}= (-4/x) + C

but at x=4, v=0

Hence, C = 1

My final equation: v

^{2}= (-4/x) +1

But from the looks of it trying to find x(t) and then setting to zero seems too difficult. How else can you solve this? The answer is 2 pi seconds