newtonian mechanics - How can an object's instantaneous speed be zero and it's instantaneous acceleration be nonzero?

I'm studying for my upcoming physics course and ran across this concept - I'd love an explanation.

Answer

Suppose you throw a ball upwards at some velocity $v$. When you catch it again it's traveling downwards at (ignoring air resistance) a velocity of $-v$. So somewhere in between throwing and catching the ball it must have been stationary for a moment i.e. it's instantaneous velocity was zero. Obviously this was at the top of its travel.

When you throw the ball it immediately starts being accelerated downwards by the Earth's gravity, so it has a constant acceleration downwards of $-9.81ms^{-2}$ (the acceleration is negative because it's reducing the velocity of the ball).

So this is an example of how there can be a non-zero acceleration (of $-9.81ms^{-2}$) but there can be a moment when the ball's instantaneous velocity is zero.