In simple terms
A friendly intro before the formal notes — no formulas yet.
Non-uniform motion
Cambridge 9702 Paper 2 — Non-uniform motion (3.2). Senpai Corner diagram-backed pilot with premium structure and live visuals.
- 1
Momentum is a vector quantity, meaning it has both magnitude and direction.
- 2
Mass is a measure of an object's inertia – its resistance to changes in motion.
- 3
Newton's Second Law can be rephrased: resultant force equals the rate of change of momentum (). This is the most general form of the law, as it applies even when mass is changing (e.g., a rocket burning fuel), whereas assumes constant mass.
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This definition is particularly useful when mass isn't constant or in impulse calculations.
What this topic covers
The official Cambridge syllabus points this lesson works through.
- 3.2.1
Show a qualitative understanding of frictional forces and viscous/drag forces including air resistance (no treatment of the coefficients of friction and viscosity is required, and a simple model of drag force increasing as speed increases is sufficient)
- 3.2.2
Describe and explain qualitatively the motion of objects in a uniform gravitational field with air resistance
- 3.2.3
Understand that objects moving against a resistive force may reach a terminal (constant) velocity
Explore the concept
Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.
Step-synced diagram — highlights what to look for in the simulation above.
Step 1
Momentum is a vector quantity, meaning it has both magnitude and direction.
12 more simulations for this topic — run them in the Simulations section below
Simulations
Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.
12 simulations · 4 to start with
Start herein this order — each one shows a different piece of the topic
- The Physics ClassroomStart here · 19702 3.2 · IB A.2 · IB A.1
Falling Bodies - 1D
A numerical model of a fall with air resistance: set the mass, initial height, initial velocity, profile area, drag coefficient and air density
Why this one: Add drag and the v–t graph bends over; a bigger area or drag coefficient lowers the terminal speed.
Try this
- Set the drag coefficient to zero and run the fall.
- Add drag and watch the velocity level off.
- Increase the profile area and compare.
Look for Terminal velocity is reached when the drag force equals the weight.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- PhETStart here · 29702 3.2
Projectile Motion
Switch air resistance on and compare the same launch with and without drag.
Why this one: Same launch with drag on: the range shrinks and the path comes down steeper than it went up.
Try this
- Fire at 20 m/s, 45° with drag off, then on — compare the two ranges.
- Raise the drag coefficient and fire straight up — watch the descent speed level off.
- Pick the bowling ball, then the baseball — same launch, different paths.
Look for Drag grows with speed, so the path becomes asymmetric and a falling object approaches terminal velocity.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
- The Physics ClassroomStart here · 39702 3.1 · 9702 3.2 · IB A.2
Rocket Sledder
Vary the sledder's mass, the parachute size, the applied force and the friction; speed, acceleration and force values display as it moves
Why this one: Thrust fixed, parachute open: speed stops rising once resistive forces balance the push.
Try this
- Apply a force with no parachute and read the acceleration.
- Open the parachute and watch the speed level off.
- Increase the mass and compare the acceleration.
Look for Speed stops rising when air resistance plus friction equal the applied force.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- 3JCN PhysicsStart here · 49702 3.2 · IB A.2
Viscosity
Drop spheres through fluids of different viscosity; see terminal velocity
Why this one: A sphere in fluid reaches terminal velocity when drag plus upthrust equal its weight; thicker fluid, slower fall.
Try this
- Drop a sphere through the fluid and watch it reach terminal velocity.
- Increase the viscosity and compare the terminal velocity.
Look for Terminal velocity is reached when drag plus upthrust balance weight, and it falls as viscosity rises.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
More simulations8 more on this topic — core ones first
- PhETCoreJava · best on a laptop9702 3.1–3.2 · IB A.2
Forces in 1 Dimension
Push a crate or fridge with a chosen applied force; read friction, net force, and the acceleration and velocity graphs.
Try this
- Apply a small force — the crate does not move; read the friction force matching it.
- Increase the force past the friction limit — acceleration appears on the graph.
- Hold the force steady — the velocity graph becomes a straight ramp.
Look for Static friction cancels small pushes; once moving, net force = ma and velocity grows linearly.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
- PhETCoreJava · best on a laptop9702 3.1–3.2 · IB A.2
Forces and Motion
Push a crate or fridge across a surface with chosen friction; see the free-body diagram and the force, velocity and acceleration graphs.
Try this
- Push the crate with 100 N — compare applied force with friction on the free-body diagram.
- Set friction to zero — the crate accelerates for as long as you push.
- Swap the crate for the fridge — the same push gives less acceleration.
Look for Net force, not applied force, sets acceleration: a = (F − friction)/m.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
- The Physics ClassroomCore9702 2.1 · 9702 3.2 · IB A.1
Trajectory
Projectile motion with air resistance: set the launch and drag parameters and compare the trajectory with the no-drag case
Try this
- Launch with drag off and note the range.
- Turn drag on with the same launch and compare the range.
- Change the launch parameters and repeat.
Look for Air resistance shortens the range and makes the descent steeper than the ascent.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- SimuPhysicsCore9702 2.1 · 9702 3.2 · IB A.1
Uniform and Non-Uniform Velocity
Objects moving uniformly run alongside objects whose velocity changes, with graphs that make the distinction precise
Try this
- Compare the position graphs of the two objects.
- Compare the velocity graphs.
- Compare an object at constant speed with one at constant velocity.
Look for Constant velocity means a straight position graph; changing velocity means a curved one.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
- 3JCN PhysicsCore9702 2.1 · 9702 3.2 · IB A.1
Projectile Motion
Set launch angle, speed, height, gravity and drag; trace the path and inspect range, time and height
Try this
- Set the launch angle to 45° with no drag and read the range.
- Try 30° and 60° at the same speed and compare the ranges.
- Raise the launch height and read the time of flight.
- Turn on drag and compare range and maximum height with the no-drag path.
Look for Without drag the path is a parabola with equal ranges at complementary angles; drag shortens the range and lowers the peak.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- PhysicsHubCore9702 2.1 · 9702 3.2 · 9702 5.2
Ball Gravity
Ball falls and bounces; adjust g, mass, wind acceleration, friction coefficient and restitution to compare free fall, weight vs mass and energy loss per bounce
Try this
- Change the mass with g fixed and compare the fall.
- Increase g.
- Lower the restitution and count the bounces.
Look for Fall time depends on g and not on mass; each bounce loses a fixed fraction of the kinetic energy.
PhysicsHub (@mattqdev) · MIT
Key formulas
Tap any symbol to reveal exactly what it means and its units.
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Full topic notes
Formal explanation with the rigour you need for the exam.
What is Non-Uniform Motion?
Non-uniform motion occurs whenever an object experiences a change in its velocity. This means it is either accelerating (speeding up), decelerating (slowing down), or changing its direction of travel. Crucially, a resultant (net) force must be acting on the object to cause this change; without it, velocity remains constant.
Newton's Laws of Motion
Sir Isaac Newton's three laws form the bedrock of understanding how forces cause motion. His First Law states that an object will maintain its state of rest or constant velocity unless acted upon by a resultant force. This perfectly explains why non-uniform motion requires a net force.
Newton's Second Law provides a quantitative link between force, mass, and acceleration. It tells us that the acceleration an object experiences is directly proportional to the resultant force applied to it, and inversely proportional to its mass. Crucially, both force and acceleration are vector quantities, and the direction of acceleration always matches the direction of the resultant force.
Momentum: The Quantity of Motion
Beyond just , force can also be understood in terms of momentum. Momentum () is a fundamental vector quantity that measures an object's 'quantity of motion'. It depends on both an object's mass and its velocity. The more massive or faster an object is, the greater its momentum.
Momentum is a vector quantity, meaning it has both magnitude and direction.
Mass is a measure of an object's inertia – its resistance to changes in motion.
Newton's Second Law can be rephrased: resultant force equals the rate of change of momentum (). This is the most general form of the law, as it applies even when mass is changing (e.g., a rocket burning fuel), whereas assumes constant mass.
This definition is particularly useful when mass isn't constant or in impulse calculations.
Action-Reaction Pairs: Newton's Third Law
Newton's Third Law describes how forces always occur in pairs: 'For every action, there is an equal and opposite reaction.' When object A exerts a force on object B, object B simultaneously exerts a force on object A that is equal in magnitude and opposite in direction. These forces are critical for understanding interactions. A common point of confusion is to think these forces cancel out. They do not, because they always act on different objects and therefore cannot be combined to find a resultant force on a single object.
Weight and Falling Objects
Weight () is the force of gravity acting on an object, pulling it towards the centre of the Earth. It's distinct from mass, which is a measure of matter. For objects near Earth's surface, we calculate weight using the object's mass and the acceleration due to gravity.
When an object falls through a fluid like air, its motion is non-uniform. Initially, its weight is the dominant force, causing it to accelerate rapidly. However, as its velocity increases, resistive forces such as air resistance (drag) and upthrust begin to grow significantly.
Air resistance opposes motion through a fluid and increases with speed.
Upthrust is an upward force exerted by a fluid, acting against an object's weight.
The magnitude of air resistance depends on speed, shape, and fluid properties.
Both air resistance and upthrust work to reduce the net downward force on a falling object.
Terminal Velocity Explained
As resistive forces increase, the resultant downward force on the falling object decreases. This, in turn, reduces its acceleration. Eventually, the upward resistive forces perfectly balance the downward driving forces (like weight). At this point, the resultant force becomes zero.
Terminal velocity is the constant, maximum velocity an object achieves when the resultant force acting on it is zero. With no net force, there is no further acceleration, and the object continues to fall at a steady speed.
The motion of a falling object can be visualised on a velocity-time graph. Initially, the gradient is steep and constant (equal to 'g' in a vacuum, slightly less in air), representing high acceleration. As speed increases, air resistance builds, so the net force and acceleration decrease, and the gradient of the graph becomes shallower. Finally, when terminal velocity is reached, the acceleration is zero, and the graph becomes a horizontal line.
Resistive forces increase with speed, reducing the net force and acceleration.
Terminal velocity occurs when resistive forces exactly balance driving forces (e.g., weight).
At terminal velocity, the resultant force is zero, meaning acceleration is zero.
The object then moves at its maximum possible constant speed through the fluid.
Projectile Motion with Air Resistance
For objects undergoing projectile motion, like a ball thrown through the air, air resistance has a significant effect on the trajectory. In an ideal vacuum, a projectile follows a perfectly symmetrical parabolic path. However, air resistance, a form of drag, opposes the velocity vector at all points. This continuous opposition to motion removes energy from the projectile, leading to several key differences from the ideal path.
Reduced Range and Height: The horizontal range and the maximum vertical height achieved are both significantly reduced.
Asymmetrical Trajectory: The path is no longer a perfect parabola. The angle of descent is steeper than the angle of ascent.
Shorter Time of Flight: The overall time the projectile spends in the air is reduced.
Reduced Speed: The speed of the projectile at any given height on its way down is less than its speed at the same height on the way up.
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
A 2.5 kg object accelerates uniformly from rest to 15 m/s in 3.0 seconds due to a constant resultant force. Calculate the magnitude of this resultant force.
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Identify knowns and unknowns:
An 80.0 kg skydiver jumps from a plane. Assume the acceleration due to gravity, g, is 9.81 m/s². (a) Calculate the skydiver's weight. (b) At an instant during the fall, the air resistance is 600 N. Calculate the resultant downward force and the skydiver's acceleration at this moment. (c) What is the magnitude of the air resistance when the skydiver reaches terminal velocity?
- 1
(a) Calculate the weight:
How it all connects
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Glossary
Key terms for this topic — skim now; the Check step will test them.
- First Law
His First Law states that an object will maintain its state of rest or constant velocity unless acted upon by a resultant force.
- Second Law
Newton's Second Law provides a quantitative link between force, mass, and acceleration. It tells us that the acceleration an object experiences is directly proportional to the resultant force applied to it, and inversely proportional to its mass.
- Third Law
Newton's Third Law describes how forces always occur in pairs: 'For every action, there is an equal and opposite reaction.' When object A exerts a force on object B, object B simultaneously exerts a force on object A that is equal in magnitude and opposite in direction.
- Weight
Weight () is the force of gravity acting on an object, pulling it towards the centre of the Earth.
- Terminal velocity
Terminal velocity is the constant, maximum velocity an object achieves when the resultant force acting on it is zero.
Quick check
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Teach it back
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Teach it back
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Revision flashcards
Guess first, then flip — retrieval beats re-reading.
Key takeaways
Review these before you close the topic — retrieval beats re-reading.
Momentum is a vector quantity, meaning it has both magnitude and direction.
Mass is a measure of an object's inertia – its resistance to changes in motion.
Newton's Second Law can be rephrased: resultant force equals the rate of change of momentum (). This is the most general form of the law, as it applies even when mass is changing (e.g., a rocket burning fuel), whereas assumes constant mass.
This definition is particularly useful when mass isn't constant or in impulse calculations.
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
The parachute is fully open at time t₂. At a later time t₃ the skydiver reaches a constant velocity of 5.7 ms¯¹.
Describe and explain the variation with time of the magnitude of her acceleration between time t₂ and time t₃.
The sphere has a radius of 3.0 cm and is falling vertically downwards at a terminal velocity of 2.0 m s⁻¹ through the liquid. The drag force acting on the sphere is 0.096 N. Calculate the viscosity of the liquid.
Extra simulations & links
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Frequently asked
Checkpoint
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