What is non-uniform motion in the context of Dynamics?

Non-uniform motion refers to the movement of an object where its velocity changes over time. This can occur due to variations in speed or direction, or both. In the context of Dynamics, which is a branch of Physics studied in the Cambridge International A Levels, non-uniform motion is analyzed to understand how forces affect the motion of objects.

How does non-uniform motion differ from uniform motion?

Non-uniform motion differs from uniform motion in that the velocity of an object changes in non-uniform motion, whereas in uniform motion, the object moves at a constant speed in a straight line. In non-uniform motion, the acceleration is not zero, indicating that forces are acting on the object to change its speed or direction.

What are some examples of non-uniform motion in everyday life?

Examples of non-uniform motion include a car accelerating or decelerating on a road, a roller coaster moving along its track, and a ball thrown into the air that changes speed as it rises and falls. These examples illustrate how forces cause changes in velocity, a key concept in Dynamics for Cambridge International A Levels Physics.

How is acceleration related to non-uniform motion?

Acceleration is a crucial aspect of non-uniform motion, as it quantifies the rate of change of velocity of an object. In non-uniform motion, acceleration can be constant or variable, and it determines how quickly an object's speed or direction changes. Understanding acceleration is essential for analyzing non-uniform motion in Dynamics.

What equations are used to describe non-uniform motion in Physics?

In Physics, particularly at the Cambridge International A Levels, equations such as the kinematic equations are used to describe non-uniform motion. These equations relate displacement, initial velocity, final velocity, acceleration, and time. They help predict the future position and velocity of an object under non-uniform motion conditions.

Why is "Treating drag as constant" a common mistake in Non-uniform motion?

Why it happens: Simplification. How to avoid it: Drag INCREASES with speed. As object accelerates, drag grows, reducing net force and hence acceleration. Source: 9702 Examiner Reports 2022-2024

Why is "Saying terminal velocity means stopping" a common mistake in Non-uniform motion?

Why it happens: Confusing a = 0 with v = 0. How to avoid it: At terminal velocity, ACCELERATION = 0, but velocity is a CONSTANT non-zero value (maximum). Source: 9702 Examiner Reports 2022-2024

DynamicsCambridge International A Level Physics 9702

Non-uniform motion

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Non-Uniform Motion Study Notes — Cambridge International A Level Physics 9702 Dynamics (2025-2027 syllabus)

Drag and air resistance. Terminal velocity. Why falling objects don't accelerate forever.

What you’ll learn

Mapped to the Cambridge International A Level 9702 syllabus (2025-2027).

3.2.1 — Describe motion under air resistance.
3.2.2 — Define and find terminal velocity.
3.2.3 — Explain parachute deployment qualitatively.

Drag force

Increases with speed.

Drag. Force opposing motion through a fluid.

Magnitude. Depends on:

Speed (often $\propto v$ at low speed, $\propto v^2$ at high speed).
Cross-sectional area.
Shape (drag coefficient).
Fluid density.

Direction. Always OPPOSES motion.

Model 1 (linear, low speed). $F_d = kv$ .

Model 2 (quadratic, fast through air). $F_d = \frac{1}{2}\rho C_d A v^2$ .

Cambridge tip. State assumed model when computing.

Always opposes motion.
Increases with speed.
Linear vs quadratic models.

Terminal velocity

Drag = weight.

Definition. Maximum constant velocity reached by a falling body when drag balances weight.

At terminal velocity. $F_d = mg$ . Net force = 0. Acceleration = 0. Velocity CONSTANT (not zero — maximum).

Stages.

$t = 0$ : $v = 0$ , $F_d = 0$ , $a = g$ (max).
Intermediate: $v$ grows, $F_d$ grows, net force decreases, $a$ decreases.
$v = v_t$ : $F_d = mg$ , $a = 0$ , $v$ constant.

Calculation (linear drag). $kv_t = mg \Rightarrow v_t = mg/k$ .

Example. $m = 0.1$ kg, $k = 0.2$ kg/s → $v_t = 4.9$ m/s.

Parachute. Opening increases area dramatically → drag jumps → decelerates body → new SMALLER terminal velocity → safe landing.

Cambridge tip. Always state 'acceleration is zero, velocity is maximum constant'.

Drag = weight.
$a = 0$ , $v$ constant.
Parachute: bigger area, smaller $v_t$ .

See the full worked example for non-uniform motion →

Velocity-time graph

Curves to a horizontal asymptote.

Without drag. Straight line from origin with slope $g$ .

With drag. Curve starting at slope $g$ , gradient decreasing, approaching constant horizontal asymptote at $v_t$ .

Parachute opens. Sharp dip (deceleration), then approaches new lower asymptote.

Sketch label. Mark $v_t$ , label initial slope $g$ , label parachute deployment time.

Cambridge tip. Mark scheme rewards correctly shaped curve + labels.

A body falling through air starts with acceleration g, drag grows with speed and the velocity curve flattens to the terminal velocity v_t where drag balances weight.

Curve approaches $v_t$ asymptote.
Initial slope $g$ .
Parachute = step + new asymptote.

See the full worked example for non-uniform motion →

How it’s examined

Non-uniform motion appears every Paper 1 and Paper 2. Most-tested: qualitative description (5-6 marks), terminal velocity equation (5-7 marks), parachute story (5 marks).

Sources: Cambridge International A Level Physics 9702 syllabus (2025-2027); 9702 Examiner Reports 2022-2024; 9702/22 Oct/Nov 2024 question paper and mark scheme. Last reviewed 2026-05-11.

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Step-by-step worked examples — Non-uniform motion

Step-by-step solutions to past-paper-style questions on non-uniform motion, written exactly the way a tutor would explain them at the board.

1Reaching terminal velocity (6 marks)
Extended• Adapted from 9702/22 Oct/Nov 2024• terminal velocity
Question
Skydiver falls from rest. Initially $a = g$ . Describe how velocity and acceleration change until terminal velocity is reached. (6 marks)
Step-by-step solution
1. Step 1
  Initially velocity is zero, drag is zero. Only gravity acts. $F_{\text{net}} = mg$ , $a = g$ .
2. Step 2
  As $v$ increases, drag $F_d$ increases (drag $\propto v$ or $v^2$ ).
3. Step 3
  Net force decreases. $F_{\text{net}} = mg - F_d$ . Acceleration decreases.
4. Step 4
  At terminal velocity, drag equals weight: $F_d = mg$ . Net force = 0. Acceleration = 0. Velocity stays constant.
Answer
Velocity increases at decreasing rate; acceleration decreases from $g$ to zero. Terminal velocity reached when $F_d = mg$ .
2Terminal velocity calculation (7 marks)
Extended• terminal velocity
Question
A small ball of mass $m = 0.10$ kg experiences a drag force $F_d = kv$ where $k = 0.20$ kg/s. Find its terminal velocity. Take $g = 9.81$ . (7 marks)
Step-by-step solution
1. Step 1
  At terminal velocity, $F_d = mg$ .
  $k v_t = m g$
2. Step 2
  Solve.
  $v_t = \dfrac{mg}{k} = \dfrac{0.10 \times 9.81}{0.20} = 4.905 \text{ m/s}$
Answer
$v_t \approx 4.9$ m/s.
3Parachute deployment (5 marks)
Extended• parachute
Question
A skydiver is falling at terminal velocity. Describe what happens (qualitatively) when their parachute opens. (5 marks)
Step-by-step solution
1. Step 1
  Larger area → drag INCREASES suddenly.
2. Step 2
  Drag now > weight. Net force acts UPWARDS → DECELERATION.
3. Step 3
  Velocity decreases. Drag decreases as velocity decreases.
4. Step 4
  New equilibrium. Drag = weight again at a SMALLER terminal velocity.
5. Step 5
  Landing. Sufficiently slow new terminal velocity allows safe landing.
Answer
Drag jumps up → decelerates → slows to new (lower) terminal velocity.

Key Formulae — Non-uniform motion

The formulae you need to memorise for non-uniform motion on the Cambridge International A Level 9702 paper, with every variable defined in plain English and a note on when to use it.

Drag (linear and quadratic models)
$F_d = kv \quad \text{(low speed)} \quad \text{or} \quad F_d = \tfrac{1}{2}\rho C_d A v^2 \quad \text{(high speed)}$
$k$
drag coefficient (linear)
$\rho$
fluid density
$C_d$
drag coefficient (quadratic)
$A$
cross-sectional area
When to use
Drag increases with speed. Linear model for slow objects in viscous fluid; quadratic at higher speeds in air.
Terminal velocity
$F_d = mg \Rightarrow v_t = \dfrac{mg}{k} \text{ or } v_t = \sqrt{\dfrac{2mg}{\rho C_d A}}$
When to use
At terminal velocity, drag balances weight. Object falls at constant speed.

Key Definitions and Keywords — Non-uniform motion

Definitions to memorise and the exact keywords mark schemes credit for non-uniform motion answers — sharpened from recent examiner reports for the 2026 Cambridge International A Level 9702 sitting.

Drag (air resistance)
Examiner keyword
Resistive force opposing motion through a fluid. Magnitude depends on speed, shape, surface area.
Terminal velocity
Examiner keyword
Maximum constant velocity reached when drag equals weight (or any driving force). Net force = 0.

Common Mistakes and Misconceptions — Non-uniform motion

The traps other students keep falling into on non-uniform motion questions — taken from recent Cambridge International A Level 9702 examiner reports and mark schemes — and how to avoid them.

✕Treating drag as constant
9702 Examiner Reports 2022-2024
Why it happens
Simplification.
How to avoid it
Drag INCREASES with speed. As object accelerates, drag grows, reducing net force and hence acceleration.
✕Saying terminal velocity means stopping
9702 Examiner Reports 2022-2024
Why it happens
Confusing $a = 0$ with $v = 0$ .
How to avoid it
At terminal velocity, ACCELERATION = 0, but velocity is a CONSTANT non-zero value (maximum).

Practice questions

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Non-uniform motion — frequently asked questions

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Non-uniform motion

Short Study Notes in the form of Slides

Short Study Notes — Non-uniform motion

Detailed Notes

What you’ll learn

How it’s examined

1Reaching terminal velocity (6 marks)

2Terminal velocity calculation (7 marks)

3Parachute deployment (5 marks)

Drag (linear and quadratic models)

Terminal velocity

Drag (air resistance)

Terminal velocity

✕Treating drag as constant

✕Saying terminal velocity means stopping

Practice questions

Past paper style quiz

Assess your understanding

Video lesson

Non-uniform motion — frequently asked questions