Acceleration of a Bouncing ball when it hits the ground

The conceptual problem I am having difficulty with is something like this:

If a bouncy ball is dropped from some height $$h$$ and rebounds to a height of $$0.75h$$ in some time $$t$$ (for example), what is the balls acceleration at the instant when it hits the ground?

Here's what I think:

I assume that the initial speed of the ball is $$0 m/s$$ and that it reaches a maximum velocity just before hitting the ground. The instant the ball touches the ground, the velocity becomes $$0 m/s$$ again, after which it starts accelerating upward.

Drawing the velocity time graph, I have something like this:

Not exactly the best diagram, but I hope that it gets my idea across.

My question is then, does this mean that the acceleration at the instant that the ball hits the floor is $$\infty$$? (since slope of the v-t graph will approach $$\infty$$)