Re: How to solve variable acceleration equations?

The way you worded your question leaves it unclear as to whether you have
enough information to solve this problem.  In addition to the pieces of
information you mentioned, you also need to know the acceleration at all
points in time.  Do you have this information?  

There are three ways the acceleration for all points in time can be obtained:

1. You know it, and just forgot to mention it in your question.

2. You know the force at all times and the mass, and F=m*a.

3. You know the rate that the acceleration is changing. You'll have to
integrate once to get acceleration.  The initial acceleration will specify
the additional constant of integration.

If you know the acceleration at all points in time, the quick summary is
that you need to integrate three times and know some constants.  More
detail below:

Integrate the acceleration to get velocity.  You then need to know the
initial velocity (or the velocity at some point in time) to specify the
constant of integration.  Then you integrate once more to get distance
traveled, where the constant is the initial position.  

So, to answer the original question you would put the initial and final
values for position, the initial value for velocity and the values that
you obtained from the integrations all together and hopefully be able to
find the total time.

-Marcy LaViollette, Nathan Cappallo, and Dustin Barnard