Q.)  Can acceleration exist without velocity?

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Ans.1)  In order for there to be force, there has to be acceleration, which is, by definition, change in velocity divided by change in time.

how can there be change is velocity if the velocity is zero. This would suggest that the answer to the question is no.

However, consider throwing a ball in the air and then catching it.

When it reaches its highest point, its velocity is zero right? it has to be zero at some time, because it switches direction.

but, even when it is zero it is accelerating.

so you definitely can have acceleration without velocity.