How can Newtonian gravity be converted to m/s without prefix?

[TheNormalForc]

Before I inundate you with various elementary problems I'm facing, I need help with the concept.

Fgrav=(GMm)/(r^2)

So Fgrav is in units of Newtons, correct? How would one convert that to m/s?

 

[kkrizka]

Gravity is just a force an object with mass experiences, which can be translated to acceleration with Newton's 2nd Law, F=ma. It has nothing to do with velocity (which has units m/s). However you can turn it into units of m/s^2, which is the units of acceleration with the above mentioned law: a=F/m, therefore:
$$a_{gravity}=\frac{GM}{r^2}$$

Where M is the mass of the object that is creating the gravitational field, not the "accelerating object".