What Is the Acceleration at the Top of a Throw?

The question

A ball is thrown vertically upwards. Ignoring air resistance, what is its acceleration at the highest point of its motion?

The common wrong answer

The most common answer is zero, because “the ball stops at the top”.

That mixes up velocity and acceleration. At the top, the ball’s velocity is momentarily zero, but its acceleration is not.

The correct working

The only force acting on the ball is its weight, the whole time it’s in the air: going up, at the top, and coming down. So its acceleration is always the acceleration due to gravity:

a = g \approx 9.8\ \text{m/s}^2 \quad (\text{often taken as } 10\ \text{m/s}^2), \text{ directed downwards}

If the acceleration really were zero at the top, the ball would have zero velocity and nothing changing it, so it would hang in the air forever.

Why it works

Acceleration tells you how quickly velocity is changing, not how fast the object is moving. Just before the top, the ball is moving upwards slowly; just after, it is moving downwards slowly. Its velocity is changing from up to down, and that change is caused by the one force that never stops acting: the ball’s weight. By Newton’s second law, a constant resultant force (the weight, $mg$ ) gives a constant acceleration:

a = \frac{F}{m} = \frac{mg}{m} = g

So the acceleration is the same at every point of the flight, including the top, where only the velocity happens to be zero for an instant.

How to spot it next time

Zero velocity does not mean zero acceleration. Acceleration is the rate of change of velocity. At the top the velocity is changing from upwards to downwards, so it’s still accelerating.
On a velocity–time graph for a vertical throw, the line crosses zero at the highest point but its gradient (the acceleration) stays the same throughout.
Ask: what forces act here? If there’s a resultant force, there’s an acceleration.