1.4.5Dynamics
Free-Fall and Terminal Velocity — SQA National 5 Physics Revision Notes & Topical Questions
5 min read 5 parts Lesson 15 of 22
Part 1 of 5Forces on a Falling Object
A skydiver does not keep speeding up forever, and the reason is the growing force of air resistance.
Weight
- Weight acts downwards all the time and is calculated using W = m g, so it stays constant during a fall.
Air resistance
- Air resistance (drag) acts upwards, against the motion, and increases as the speed of the object increases.
Resultant
- The resultant force is weight minus air resistance, and Newton's second law gives the acceleration.
Free-fall
- With no air resistance the object accelerates at 9.8 m/s² regardless of its mass, as on the Moon.
Part 2 of 5Stages of a Skydive
1
At the start air resistance is almost zero, so the resultant force equals the weight and acceleration is about 9.8 m/s².
2
As speed increases air resistance grows, the resultant force gets smaller and the acceleration decreases.
3
At terminal velocity the air resistance equals the weight, the forces are balanced and the velocity is constant.
4
When the parachute opens the air resistance suddenly becomes larger than the weight, so the skydiver decelerates.
5
As speed falls the air resistance decreases until it again equals the weight, giving a new, much lower terminal velocity.
6
On landing the ground exerts a force that brings the skydiver to rest.
Part 3 of 5Velocity–Time Graph
Velocity–Time Graph
Rising curve
- The line rises steeply at first and then becomes flatter as the acceleration decreases.
Flat section
- The horizontal line shows terminal velocity, where the resultant force is zero.
After parachute
- The line drops quickly, then levels out again at a lower constant velocity.
Surface area
- A larger surface area, as with a parachute, gives more air resistance at a given speed and so a lower terminal velocity.
| Stage | Air resistance vs weight | Motion |
|---|---|---|
| Start | Much smaller | Large acceleration |
| Terminal velocity | Equal | Constant velocity |
| Parachute opens | Larger | Decelerating |
Part 4 of 5Worked Example
Question
- A skydiver of mass 80 kg (g = 9.8 N/kg) falls.
- Calculate the weight, the air resistance at terminal velocity, and the acceleration when the air resistance is 304 N.
- Weight = m g = 80 × 9.8 = 784 N.
- At terminal velocity the forces balance, so air resistance = 784 N.
- When air resistance is 304 N: resultant = 784 − 304 = 480 N, so a = 480 ÷ 80 = 6.0 m/s².
Answer
- Weight 784 N;
- terminal air resistance 784 N;
- acceleration 6.0 m/s².
Part 5 of 5Exam Checklist & Tips
1.4.5 – Key Points for the Exam
- Terminal velocity The constant velocity reached when air resistance equals the weight.
- Air resistance The frictional force of air opposing motion.
- Free-fall Motion under the influence of gravity alone.
- Drag Another name for the resisting force from a fluid such as air.
Common Mistakes
- Saying the weight decreases as the skydiver reaches terminal velocity; the weight stays constant.
- Thinking that at terminal velocity there are no forces acting, when actually there are two equal opposite forces.
- Believing heavy objects always fall faster, which is only because of air resistance.
- Stating that the skydiver stops when the parachute opens, rather than slowing to a lower terminal velocity.
Last updated:
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/s2downwards (air resistance negligible).