Question
A ball is thrown vertically upwards with a velocity of . At the highest point, what is its acceleration? Many students answer “zero” because the velocity is zero. Why is that wrong, and what is the correct answer?
Solution — Step by Step
Velocity tells us how fast the ball is moving. Acceleration tells us how fast the velocity is changing. These are two different quantities, even though they share units of “per second” somewhere.
Once the ball leaves our hand, the only force on it is gravity (we ignore air resistance for JEE/NEET unless told otherwise). Gravity always pulls downward with .
tells us the acceleration is determined by the force, not by the current velocity. Since gravity acts even when the ball is momentarily at rest at the top, the acceleration there is still pointing downward.
At the highest point, but directed downward. The acceleration is not zero — it is throughout the motion.
Why This Works
Velocity being zero just means “not moving right now.” Acceleration being zero would mean “no net force acting.” These are completely different conditions.
Think about it this way: if acceleration were zero at the top, the ball would just float there forever. The fact that it starts coming back down proves that acceleration is non-zero at that instant.
This is one of the cleanest tests of whether a student really understands the definition of acceleration vs. just memorizing formulas.
Alternative Method — Graphical View
Draw the velocity-time graph. It is a straight line with negative slope (), starting at , crossing zero at , and continuing to negative values.
The slope of this graph IS the acceleration. The slope is constant and non-zero throughout — including at the moment the line crosses the time axis. That crossing point is where , but the slope (acceleration) is unchanged.
Common mistake: Saying “at the topmost point velocity is zero, so acceleration must also be zero.” This conflates two independent quantities. A car at a red light has but if you press the accelerator, it has non-zero even before it starts moving.
Common Mistake
Students often write at the highest point in JEE Main MCQs and lose easy marks. The trap appears in roughly one shift every JEE Main attempt — examiners love it because it separates rote learners from conceptual learners.
In NEET 2023, a similar question asked about the acceleration of a particle in projectile motion at the topmost point. Students who answered “zero horizontal acceleration but vertical acceleration” got full marks. Students who said acceleration is zero lost 4 marks plus negative marking.
The fix is simple: every time we see “at the highest point” or “at the moment of stopping,” we mentally separate from before answering.