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Air resistance and terminal velocity

Key idea: Air resistance changes both the force balance and the energy pathway. Terminal velocity means zero acceleration, not zero force or zero energy transfer.

  • GCE A-Level H1 Physics 2027

H1 Physics 8867 · Lesson 3 of 3

Check your understanding

By the end of this lesson, you should be able to

  • Describe how drag changes during a fall.
  • Explain terminal velocity using resultant force.
  • Track gravitational, kinetic and thermal energy changes throughout the fall.

Learn the idea

Big question: How can a falling object keep losing gravitational potential energy after it stops speeding up?

Follow the changing force balance

Just after release, drag is small and weight gives a large downward resultant. As speed rises, drag grows, so the resultant and acceleration shrink even though the object is still speeding up.

At terminal velocity, drag equals weight. The forces have not disappeared: their vector sum is zero, so acceleration is zero and velocity is constant.

Check your understanding: If acceleration is decreasing during a fall, must speed be decreasing?

No. Speed still increases while acceleration is downward; it simply increases more slowly.

Track all energy transfers

Before terminal speed, falling reduces gravitational potential energy. Part increases kinetic energy and part is transferred to internal-energy stores by drag.

At terminal speed, kinetic energy is constant, but height continues to fall. The continuing gravitational-store decrease is therefore transferred entirely to internal-energy stores of the air, object and surroundings.

Check your understanding: At terminal speed, is power transferred by drag zero?

No. Drag acts while the object moves, so it continues to transfer energy thermally even though net force is zero.

Ideal projectile trajectory compared with motion under air resistanceTwo trajectories start with the same velocity. The ideal trajectory is higher, longer and symmetric. With drag, the trajectory is lower, shorter and asymmetric. A drag arrow points opposite to the velocity on the descending path.velocitydrag opposes velocityideal: no air resistancewith air resistance
Scroll diagram horizontally to read all labels.
For the same launch conditions and equal launch and landing heights, drag reduces maximum height and range and breaks the ideal trajectory's symmetry.

Key ideas

  • Weight remains approximately constant in a uniform field.
  • Drag depends on motion through the air and grows with speed.
  • Constant velocity follows from balanced forces, not from forces disappearing.

Relationships to know

  • resultant downward force = mg − drag
  • at terminal velocity: drag = mg and a = 0

Follow the reasoning

Worked example

Connect a measured acceleration to drag

Question: A 75 kg skydiver is falling downward at 30 m s⁻¹ with downward acceleration 2.0 m s⁻². Find the drag force and the rate at which drag transfers energy to internal stores. Use g = 9.81 m s⁻².

  1. Step 1: Write the downward resultant

    Why: Weight and drag oppose each other.

    Working: mg − D = ma, so D = m(g − a) = 75(9.81 − 2.0) = 585.75 N.

  2. Step 2: Find drag power

    Why: Drag is opposite velocity, so its magnitude times speed is the rate of thermal transfer.

    Working: Pdrag = Dv = 585.75(30) = 1.76 × 10⁴ W.

  3. Step 3: Interpret the remainder

    Why: Not all gravitational power becomes heating while speed is still rising.

    Working: Gravity transfers mgv = 2.21 × 10⁴ W; the difference 4.50 kW increases kinetic energy.

Answer: Drag is about 586 N upward and transfers energy thermally at about 17.6 kW.

Check: Drag is below the 736 N weight, so a downward resultant and increasing speed are consistent.

Now try it with support

Practise with support

A falling sphere is travelling below terminal speed. Predict what happens to drag, resultant force and acceleration as its speed rises.

Hints

  1. Weight is nearly constant.
  2. Increasing drag subtracts more from weight.
View the guided answer

Drag increases, so the downward resultant mg − drag decreases. Downward acceleration therefore decreases, although speed continues to rise until terminal velocity.

Your turn

Practise independently

Sketch and explain how weight, drag, acceleration, speed, kinetic energy and gravitational-potential-energy transfer change from release until a falling sphere reaches terminal velocity.

Check your answer

A correct account shows constant weight downward; drag rising from near zero until it equals weight; downward acceleration falling to zero; speed rising towards a constant value; kinetic energy rising then becoming constant; and gravitational potential-energy loss being shared between kinetic increase and thermal transfer, then entirely thermal transfer at terminal speed.

Common mistakes and exam guidance

Watch out for

  • Saying terminal velocity means no forces act.
  • Saying gravitational potential energy stops decreasing once speed is constant.

In an exam

  • Link each stage with ‘because’: force balance → acceleration → speed → energy change.
  • Distinguish ‘decreasing acceleration’ from ‘decreasing speed’.

Put the ideas together

Exam-style practice [7 marks]

Describe a raindrop's motion and energy transfers from release until long after it reaches terminal velocity. Your answer must refer to weight, drag, resultant force, acceleration, speed and energy stores.

Plan before you answer

  • Describe release, approach and terminal stages.
  • Keep acceleration and speed distinct.
  • Continue the energy account after kinetic energy becomes constant.
View the marking points and model answer

Marking points

  1. Weight approximately constant downward.
  2. Drag starts small and increases with speed.
  3. Downward resultant and acceleration decrease.
  4. Speed rises at a decreasing rate.
  5. At terminal speed drag equals weight and acceleration is zero.
  6. Before terminal speed, gravitational decrease becomes kinetic increase and thermal transfer.
  7. At terminal speed, gravitational decrease continues entirely as thermal transfer while kinetic energy is constant.

Model answer

At release, drag is nearly zero, so weight gives a large downward resultant and the drop accelerates. As speed rises, drag rises, reducing the resultant and acceleration; speed still rises but more slowly. When drag equals weight, resultant force and acceleration are zero, so terminal speed is constant. Before then, decreasing gravitational potential energy becomes both kinetic energy and internal energy. At terminal speed the kinetic store is constant, but gravitational potential energy continues to decrease and is transferred to internal-energy stores by drag.

Finish from memory

Three-question recap

  1. What condition defines terminal velocity?

    Check

    Drag equals weight, so resultant force and acceleration are zero.

  2. What happens to kinetic energy at terminal speed?

    Check

    It stays constant.

  3. Why does gravitational potential energy still decrease?

    Check

    The object continues moving downward and losing height.

Try this next

Sketch speed–time and acceleration–time curves for the same fall and explain their shapes.

Check the whole topicReturn to Projectile MotionReview Potential energy in a uniform gravitational field

Continue with the next resource in this course.

Course and syllabus information
Course
GCE A-Level H1 Physics
Edition
GCE A-Level H1 Physics 2027