Right at the midpoint of its motion, the cart has zero acceleration, because the net force on it is zero. so, why doesn’t the cart stay at constant velocity after reaching that point?

We can't be sure of anything, because you carefully neglected
to show us the picture, or give us any information at all.  The best
we can do is to speculate that maybe, just maybe, the cart is on a
path that begins to rise, fall, or curve past the midpoint.  If that's true,
then a component of unbalanced vertical force due to gravity, or
centripetal force due to friction with the ground, begins to appear
past that point.  Then, the net force on the cart is no longer zero,
and it begins to exhibit acceleration, either slowing down, curving,
or speeding up, depending on which way the path slopes or turns.

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