Terminal velocity is the constant speed reached by a falling object when the upward drag force exactly equals the downward weight, making the resultant force zero. At this point acceleration is zero and the object falls at constant speed — a skydiver in free fall reaches about 53 m/s.
What forces act on a falling object?
When an object falls through a fluid (air or liquid), two forces act on it:
- Weight (W) — a downward force caused by gravity, equal to mass × gravitational field strength (W = mg). For an object near Earth's surface, g ≈ 10 N/kg. Weight does not change as the object falls.
- Drag (air resistance) — an upward resistive force caused by collisions between the object and air molecules. Drag increases with speed: the faster the object moves, the more collisions per second, and the greater the drag force.
At the start of a fall, weight is much greater than drag → the resultant force is downward → the object accelerates.
As speed increases, drag increases. The resultant force (weight − drag) decreases, so acceleration decreases. Eventually, drag equals weight. Resultant force = 0. Acceleration = 0. The object falls at a constant speed: terminal velocity.
How does terminal velocity appear on a velocity–time graph?
The velocity–time graph of a falling object is one of the most important GCSE graphs to recognise:
| Section of graph | Shape | What is happening |
|---|---|---|
| 0 to A | Steep curve, slope decreasing | Accelerating: weight > drag; resultant force falls as speed increases |
| A onward | Horizontal line | Terminal velocity: weight = drag; resultant force = 0; constant speed |
The gradient of the curve decreases continuously (from steep to flat) because the resultant force — and therefore the acceleration — decreases as speed rises. The curve becomes horizontal (gradient = 0) at terminal velocity.
This shape is distinctly different from an object in free fall with no air resistance (which would be a straight, steeper line), or from uniform acceleration (a straight line with constant gradient).
What happens when a skydiver opens a parachute?
A skydiver's journey illustrates two different terminal velocities:
Phase 1 — free fall: The skydiver jumps and accelerates. As speed increases, drag increases. Eventually drag = weight and the skydiver reaches terminal velocity at approximately 53–60 m/s (about 190 km/h), depending on body position (arms and legs spread creates more drag than a streamlined dive).
Phase 2 — parachute opens: Opening the parachute dramatically increases the cross-sectional area and therefore the drag force. At the instant the parachute opens, drag greatly exceeds weight → the resultant force is upward → the skydiver decelerates (speed falls). On the velocity–time graph, the line drops sharply.
As speed falls, drag decreases again. Eventually a new equilibrium is reached where drag (still large because of the parachute area) once again equals weight, but at a much lower speed — approximately 5–7 m/s, which is safe for landing.
Phase 3 — second terminal velocity: The skydiver reaches a second, much lower terminal velocity and descends at constant speed until landing.
On the velocity–time graph, the complete journey looks like:
- Curved section rising to a plateau (first terminal velocity ~53 m/s).
- Sharp drop when parachute opens (deceleration).
- Rise to a lower plateau (second terminal velocity ~6 m/s).
What factors affect the terminal velocity of an object?
| Factor | Effect on terminal velocity | Reason |
|---|---|---|
| Mass | Heavier object → higher terminal velocity | Greater weight requires greater drag to balance; greater drag requires higher speed |
| Cross-sectional area | Larger area → lower terminal velocity | More drag for a given speed; balance with weight reached at lower speed |
| Shape | Streamlined shape → higher terminal velocity | Less drag for a given speed; more speed needed to generate enough drag to equal weight |
| Fluid density | Denser fluid → lower terminal velocity | More drag per collision; balance reached at lower speed |
How do you calculate the drag force at terminal velocity?
At terminal velocity, the resultant force is zero, so drag exactly equals weight:
Drag = Weight = mg
Worked example: A parachutist with equipment has a total mass of 90 kg. Calculate the drag force at terminal velocity.
Weight = mg = 90 × 10 = 900 N At terminal velocity: Drag = 900 N (upward)
This means the parachute must generate 900 N of drag for the parachutist to descend at constant speed. A larger parachute, or a denser atmosphere, would achieve this at a lower terminal velocity.
Frequently asked questions
What is terminal velocity in GCSE physics?
Terminal velocity is the constant speed reached by a falling object when the drag force acting upward exactly balances the weight acting downward. At this point, the resultant force on the object is zero, so by Newton's second law (F = ma), the acceleration is zero and speed remains constant. Different objects reach different terminal velocities depending on their mass, shape, and cross-sectional area.
Why does a skydiver slow down when a parachute opens?
When the parachute opens, it dramatically increases the cross-sectional area of the skydiver, which enormously increases the drag force. At the moment of opening, drag is much greater than weight, giving a net upward resultant force. This decelerates the skydiver — speed falls. As speed falls, drag decreases until drag once again equals weight at a much lower speed (the second, lower terminal velocity). The skydiver then descends at this lower constant speed, which is safe for landing.
Why does acceleration decrease as a falling object speeds up?
By Newton's second law, resultant force = mass × acceleration (F = ma), so acceleration = F ÷ m. As a falling object speeds up, drag increases (drag depends on speed). The resultant downward force (weight − drag) therefore decreases, so the acceleration (= resultant force ÷ mass) also decreases. The object is still accelerating — it is still getting faster — but more slowly than before. When drag equals weight, the resultant force reaches zero and acceleration falls to zero: the object has reached terminal velocity.
What does the velocity–time graph for a falling object look like?
The velocity–time graph for an object falling through air starts as a curve with a steep gradient (high acceleration when drag is small) that gradually flattens as drag increases and reduces the net force. The curve eventually becomes a horizontal straight line at the terminal velocity — the gradient is zero, confirming zero acceleration and constant speed. If a parachute opens, the graph shows a sharp downward curve (deceleration) followed by another, lower horizontal line at the new terminal velocity.
For Socratic GCSE physics with Professor Newton — predict what the forces look like before reading the velocity–time graph — visit aitutors.me.