How does the acceleration of a cart depend on the net force acing on the cart if the total mass is constant?

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Initially, Newton defined his second law of motion in terms of the rate of change in an object's momentum:

(Pf -Pi)/t = Fnet

Subsequently he developed the concept further to

(mVf - mVi)/t = Fnet  or m(Vf - Vi)/t = Fnet

So, (Vf - Vi)/t = Fnet/m

by defining the rate of change in the velocity as acceleration we get the current form of the  second law:

a = Fnet/m

From this we can see that if m is constant then a is directly proportional to Fnet.  Increasing Fnet causes an increase in the acceleration.

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