# Acceleration as a function of position, and time taken to travel a distance

I've been doing a problem that requires me to find the time taken to travel a certain distance if I know the initial acceleration of a body at the starting position and its initial velocity (starts from rest). The acceleration is a function of position a=-GM/(Ro^2).

So say a body is released from rest a distance Ro from a point mass, and it's initial acceleration is that stated above- how would I go about finding the time taken to travel this distance (from Ro to the origin.

Thanks.

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tiny-tim
Homework Helper
hi jmz34! so r'' = -GM/r2 ?

multiply both sides by r' …

r'r'' = -GMr'/r2

… and integrate hi jmz34! so r'' = -GM/r2 ?

multiply both sides by r' …

r'r'' = -GMr'/r2

… and integrate Using this method I did this:

d/dt(0.5*(r')^2)=(-GM/r^2)r'

then integrated once and simplified to get

(dr/dt)^2=2GM/r

solving this for t gives:

t=(1/3)*SQRT(2/GM)*Ro^(3/2)

If you could have a quick look at my method I'd be very grateful.

Thanks alot.

tiny-tim
Homework Helper
Using this method I did this:

d/dt(0.5*(r')^2)=(-GM/r^2)r'

then integrated once and simplified to get

(dr/dt)^2=2GM/r.
yes, but after that i get a bit lost …

you seem to have lost r completely, and you don't have a constant of integration 