The big idea: Anything moving through air or water feels a drag force — a fluid resistance that always pushes against the motion.
Drag grows as you go faster. A falling object speeds up until the drag equals its weight — then it stops accelerating and falls at a steady terminal velocity.
What 'drag' means: Drag (also called fluid resistance or air resistance) is the friction-like force from the air or liquid an object pushes through. A 'fluid' just means a gas or a liquid.
Spot it on a v–t graph: A falling object with air resistance gives a v–t curve that starts steep, then bends over and goes flat. The flat part is the terminal velocity — drag now balances weight.
Two forces act on a falling object: its weight pulling down, and the drag pushing up (against the motion). Terminal velocity is reached when these two are equal, so the resultant force is zero.
- weight — the downward pull of gravity (N)
- mass (kg)
- gravitational field strength, 9.8 N kg⁻¹ near Earth
| Stage of the fall | Weight vs drag | Resultant force | What happens |
|---|---|---|---|
| Just released | weight ≫ drag (drag tiny) | large, downward | speeds up fast (≈ free fall) |
| Speeding up | weight > drag (drag growing) | smaller, downward | still speeds up, but less |
| Terminal velocity | weight = drag | zero | constant velocity (a = 0) |
The key condition: Terminal velocity ⇒ drag = weight ⇒ resultant force = 0 ⇒ acceleration = 0.
Constant velocity does not mean no forces — it means the forces cancel.
IB-style question — is it at terminal velocity?
A raindrop of mass 5.0 × 10⁻⁵ kg falls and reaches a steady speed. Take g = 9.8 N kg⁻¹. (a) Find its weight. (b) State the size of the drag force on it at terminal velocity.
Solution
- (a) Start with the given formula for weight:
- Put in the numbers:
- Work it out — keep the unit:
- (b) At terminal velocity the drag balances the weight (resultant = 0), so the drag is the same size:
Final answer
(a) weight = 4.9 × 10⁻⁴ N. (b) drag = 4.9 × 10⁻⁴ N (equal to the weight, acting upward).
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How this is tested: Air resistance is usually a qualitative Paper 1A multiple-choice question, not a calculation.
- On a falling body: they ask you to describe the v–t curve, or to say why the acceleration falls to zero. - On a projectile: they ask how air resistance changes the path (the next micro builds the no-resistance case first).
Classic trap: thinking a constant terminal velocity means no forces. It means the forces are balanced.
A falling object's velocity rises steeply at first, then levels off at the terminal velocity — the slope (its acceleration) falls to zero:
Equivalently, the acceleration of a falling object does not stay at g — it falls towards zero as drag builds up:
IB-style question — evaluate the statements
A skydiver falls from rest and, after some time, reaches a steady terminal velocity. Which statements are correct?
(I) The drag force on her increases as she speeds up.
(II) At terminal velocity the resultant force on her is zero.
(III) At terminal velocity her weight is zero.
Check each statement
- (I) Drag grows with speed — true. ✓
- (II) Terminal velocity means drag = weight, so the forces cancel → resultant = 0 — true. ✓
- (III) Her weight is mg and does not change as she falls; it is the drag that has grown to match it, not the weight that has vanished — false. ✗
Final answer
I and II only. Weight stays the same (mg) the whole way down — at terminal velocity the drag has grown to balance it.