Physics 9702 · Paper 1

Air Resistance & Terminal Velocity

Real falling objects push through air. (drag) acts against the motion and increases with speed.
That one fact changes the whole fall: the acceleration is no longer constant, and the speed stops rising at a limit called .

The three stages of the fall

A skydiver falling belly-down through the sky, with a weight arrow pointing down and a drag arrow pointing up. — A falling body feels two forces: weight pulling down (always the same) and drag pushing up (which grows with speed). Terminal velocity is when the two balance.

At the start: the speed is low, so drag is small. The resultant force is nearly the whole weight, so the acceleration is nearly $g$ .
As it speeds up: drag increases. The resultant force (weight − drag) gets smaller, so the acceleration decreases.
At terminal velocity: drag has grown until it equals the weight. The resultant force is zero, the acceleration is zero, and the speed stays constant.

Terminal velocity is a force balance: weight stays fixed while drag grows, until drag equals weight and the resultant is zero.

The gradient of this curve is the acceleration. It starts at g, gets smaller as drag builds up, and reaches zero at terminal velocity.

Terminal velocity is a force balance, not a speed limit built into gravity. The reasoning chain to write: speed up → more drag → smaller resultant force → smaller acceleration → zero.

Common mistake

“The acceleration becomes negative” is wrong. The acceleration decreases toward zero: the object never slows down on the way to terminal velocity, it only stops speeding up.

The exam's explain question

The standard question gives a SUVAT prediction and asks why the real speed is lower. The answer is the reasoning chain, step by step.

Your turn— tap to reveal the worked answer (9702/21/O/N/23 Q2(b))

A tennis ball is released from rest at a height of 500 m. A passenger uses $v^2 = u^2 + 2as$ to predict an impact speed of about 100 m s⁻¹. Explain why the actual speed is much lower. (9702/21/O/N/23 Q2(b), 3 marks)

Air resistance acts on the ball, and it increases with speed.
So the resultant force on the ball is less than its weight.
So the acceleration is less than g, and the final speed is less than 100 m s⁻¹.

The mark scheme does not claim the ball reaches terminal velocity: over 500 m it may not get there. Write “resultant force < weight, so acceleration < g” and stop.

The same chain, reversed, explains why a falling object's v-t curve bends over: the gradient (the acceleration) shrinks as drag builds up, which is exactly the curve in the figure above.

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