The big idea: A skydiver doesn't speed up forever. She falls faster and faster at first, then settles to a steady speed and stops speeding up. That top speed is the terminal velocity.
Why it stops speeding up: Moving through air (or water) gives a drag force — 'air resistance' — that pushes against the motion and grows as you go faster.
A falling object keeps speeding up until the drag has grown to equal its weight. Then the forces balance and the speed holds steady.
The weight stays the same the whole way down; the drag grows until it equals the weight — then the forces balance (net = 0) and the speed stops changing.
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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.
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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.
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 drag force on it at that steady speed.
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How this is tested — air resistance is usually a qualitative Paper 1A multiple-choice question, not a calculation. It shows up two ways:
A falling body
- Describe the v–t curve (steep → flat).
- Say why the acceleration falls to zero.
A projectile
- How air resistance changes the path.
- Range and peak height both drop.
The classic trap: A constant terminal velocity does not mean no forces. Weight and drag both act — they are equal and opposite, so they balance (resultant = 0).
A falling object's velocity rises steeply at first, then levels off at the terminal velocity — the slope (its acceleration) falls to zero:
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Equivalently, the acceleration of a falling object does not stay at g — it falls towards zero as drag builds up:
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A skydiver falls from rest and reaches a steady terminal velocity. Which are correct? (I) The drag on her increases as she speeds up. (II) At terminal velocity the resultant force is zero. (III) At terminal velocity her weight is zero.
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