This is for an atwood machine that is moving... so the complete question is- When an Atwood Machine is moving, what is the shape of a velocity-versus-time plot for the motion? Why?

I had to look up "Atwood Machine" - I hadn't heard of this term before. So thanks for helping me learn something new today!

An Atwood machine is basically an idealized pulley system, with two masses suspended by a string over a pulley. If you apply ΣF = ma, the term ΣF is the difference in weights between the two masses, and m is the total mass of the system (sum of the two masses). If the weights are not equal, then a is a non-zero constant. So the question boils down to this: what is the shape of the velocity-time curve for constant acceleration? Can you answer this now?