When I shoot a ball vertically upward, its velocity is decreasing since there is a downward acceleration of about $9.8\,\mathrm{ms}^{-2}$.
I have read that at the top most point, when $v = 0$, the acceleration is still $9.8\,\mathrm{ms}^{-2}$ in the downward direction where $v=0$. That is, the acceleration is still the same.
But at the highest point, the ball is stationary, so it is not even moving. How can it accelerate?
Best Answer
You throw the ball upwards with velocity $v$ and it returns to your hand with velocity $-v$. Let's draw a graph showing the velocity as a function of time:
Acceleration is defined as:
$$ a = \frac{dv}{dt} $$
so it is the gradient of the line in this graph. The velocity-time line is straight so the gradient is constant which means the acceleration is constant. The gradient is just the gravitational acceleration $9.81$ m/s$^2$.
The point is that the gradient, and hence the acceleration, does not depend on $v$ at all. So it is the same value of $9.81$ m/s$^2$ when $v = 0$ just as it is at all other values of $v$.