Skip to content
Dabour HubLEARN · PRACTICE · EXPLORESign inStudent

1.2.7Forces and Motion

Terminal Velocity

5 min read 9 parts Lesson 1 of 26 Unit quiz

0%read

Section 1 of 9Forces on a falling object

Two forces act on an object falling through air or another fluid: its weight W = mg downwards, and the fluid's drag (air resistance) upwards. Drag increases as the speed rises, and also depends on the shape and cross-sectional area of the object.

Section 2 of 9The stages of a skydive

1Start
Start speed is zero, so drag is zero. The resultant force is the full weight, and the acceleration is g (9.8 m/s2).
2Speeding up
Speeding up as speed grows, drag grows.
  • The resultant force (weight − drag) gets smaller, so acceleration decreases, although the speed is still rising.
3Terminal velocity
Terminal velocity drag has grown until it equals the weight.
  • The resultant force is zero, so acceleration is zero and the speed is constant.
  • This steady speed is the terminal velocity.
4Parachute opens
Parachute opens drag suddenly becomes much larger than weight, so the resultant is upwards and the skydiver decelerates.
5New terminal velocity
New terminal velocity as speed falls, drag falls until it again equals weight, at a much lower speed suitable for landing.

At terminal velocity the air pushes up with a force exactly equal to the weight.

1
This can be understood as the object pushing air out of its way,
  • and the air pushing back; the faster the object moves, the more air it must push aside each second,
  • so the drag increases.
2
The idea applies in liquids as well: a ball bearing dropped into glycerine reaches terminal velocity within a few centimetres and is a common school investigation,
  • where the time to fall between two marks on the tube gives the terminal speed.

Section 3 of 9Speed–time graph

The graph starts at the origin with a steep gradient (acceleration g).

Speed–time graph
The curve then bends over, with the gradient decreasing, until it becomes a horizontal line at terminal velocity.
When the parachute opens the graph falls steeply, then flattens at the lower terminal speed.
The gradient at any moment equals the acceleration, and the area under the graph equals the distance fallen.

Compare a skydiver in a spread-eagled position with the same skydiver in a head-down position.

Speed–time graph
The head-down position has a smaller area facing the air,
  • so drag at a given speed is smaller and terminal velocity is greater, roughly 55 m/s compared with 90 m/s or more.
Sky divers change position to control their speed and to move closer to or further from others during formations.

Section 4 of 9What affects terminal velocity

What affects terminal velocity
A bigger weight (more mass) means a larger drag is needed to balance it, so a higher terminal velocity.
A bigger cross-section area or a less streamlined shape gives more drag at the same speed, so a lower terminal velocity.
A denser fluid gives more drag and a lower terminal velocity.

The same ideas apply to a ball bearing falling through oil, where terminal velocity is reached in a short distance.

Reading the graph

  • if the line is straight and steep at the start, the acceleration is about 9.8 m/s2.
  • If the gradient has become zero, the object has reached terminal velocity.
  • The distance fallen between two times is the area under the graph, which can be estimated by counting squares.

Section 5 of 9Cars and cyclists

A car also has a top speed at which driving force equals total drag. Streamlined designs reduce drag, allowing higher speed or less fuel use at the same speed.

Section 6 of 9Common description for exams

Always say that weight is equal and opposite to drag, that the resultant force is zero, and that the object moves at constant velocity. Mentioning that acceleration is zero but the object is still moving is the key point.

Remember that drag does not push upwards because of gravity; it opposes the motion, so it acts upwards only because the object is moving down. For a rising object, drag acts downwards. A ball thrown upwards therefore decelerates by more than g on the way up and by less than g on the way down.

Section 7 of 9Worked examples

  1. A skydiver of mass 75 kg reaches terminal velocity. Find the drag force (g = 9.8 N/kg).

  2. A 60 kg parachutist has drag of 400 N at one moment. Find the acceleration and its direction (g = 9.8 N/kg).

  3. After opening the parachute the drag is 1800 N on a skydiver of weight 800 N, total mass 82 kg. Find the acceleration.

Section 8 of 9Key terms

TermMeaning
DragFrictional force from air or liquid opposing motion.
Terminal velocityConstant speed when drag equals weight.
Resultant forceNet force on an object.
StreamlinedShaped to reduce drag.
Cross-sectional areaArea facing the oncoming fluid.

Section 9 of 9Exam technique

1
Saying the skydiver stops accelerating because gravity stops: weight still acts.
2
Thinking terminal velocity means zero speed.
3
Saying heavier objects have the same terminal velocity regardless of shape.
4
Forgetting that drag depends on speed.
5
Drawing the graph with a horizontal line from the start.
Physics 0625 & 9702 SUVAT Mastery Graph Interpretation

Constant Acceleration Equations (SUVAT) & Slopes

v = u + at  |  s = ut + ½at2  |  v2 = u2 + 2as  |  s = ½(u + v)t

  • Displacement-Time Graph: Gradient = Velocity (curve = accelerating).
  • Velocity-Time Graph: Gradient = Acceleration; Area under curve = Distance travelled / Displacement.
  • Free Fall in vacuum: a = g ≈ 9.81 m/s2 downwards (air resistance negligible).