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I'm trying to calculate the displacement d of a plane as it accelerates towards lift-off velocity.

The acceleration is given by the function a = a

I can't seem to find a way to integrate the equation above so that I get the plane's velocity nor it's displacement.

The answer is meant to be:

d = - ln (1 - kv

The acceleration is given by the function a = a

_{0}- kv^{2}where a_{0}is the constant acceleration from the plane's engine and the term -kv^{2}is caused by air resistance.I can't seem to find a way to integrate the equation above so that I get the plane's velocity nor it's displacement.

The answer is meant to be:

d = - ln (1 - kv

^{2}/ a_{0}) / 2k
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