Why is acceleration not zero when velocity is zero?
Short answer: Gravity never switches off. v = 0 for an instant, but v is still changing at 9.8 m/s² downward.
The trap
The wrong idea
“If velocity is zero at an instant, acceleration must be zero too.”
It sounds reasonable, and a lot of JEE/NEET aspirants carry it into the exam. Here's a one-question check, then the explanation that makes it click.
Quick check
Try it before you peek
A ball thrown up reaches its highest point. Its acceleration there is:
- Zero
- g downward
- g upward
Show the answer
B. g downward
Gravity never switches off. v = 0 for an instant, but v is still changing at 9.8 m/s² downward.
The click
Velocity and acceleration answer two different questions. Velocity says how fast and in which direction something moves right now. Acceleration says how quickly that velocity is changing. A quantity can be zero at an instant while its rate of change is not, just as a car's velocity passes through zero at the moment it changes from moving forward to reversing.
Take a ball thrown straight up. On the way up its velocity points upward and shrinks by about 9.8 m/s every second. On the way down it points downward and grows by 9.8 m/s every second. At the very top the velocity is zero for one instant, but the only force acting (ignoring air) is still the ball's weight, mg, pointing down. By Newton's second law, a = F/m = g, downward, at every point of the flight, including the top.
If the acceleration really were zero at the top, the velocity would stop changing and the ball would hang in the air forever. It doesn't, which is the quickest sanity check.
The general rule is a = dv/dt. A zero value of v says nothing about the slope of v against t. On a velocity–time graph of the throw, the top is where the straight line crosses the time axis, and the slope there is still −g.
Got this one? The Knot Scan finds the misconception you don't know you have, in 8 questions.