Syllabus coverage
- Explain linear motion in terms of movement of a body in a straight or curved line where all parts move the same distance in the same direction over the same time
- Explain linear motion as created by an external force that passes through the centre of mass
- Describe, calculate and compare distance, displacement, speed, velocity, acceleration and momentum
- Explain scalar quantities and vector quantities
- Draw and interpret graphs of linear motion involving distance, displacement, speed, velocity and time
Part of the AS Level PE 8386 syllabus 8386.
What linear motion is — and what it is not
Linear motion is movement of a body in a straight or curved line where all parts of the body move the same distance in the same direction over the same time. Nothing rotates and every part of the performer covers the same ground at the same speed.
A sprinter travelling down the home straight is in linear motion. A tumble turn in competitive swimming is not, because the swimmer rotates about an axis while different parts of the body cover different distances.
Linear motion is created by an external force that passes through the centre of mass of the body. A force that passes outside the centre of mass produces rotation instead, which is angular motion.
- Straight line: a 100 m sprinter on the straight
- Curved line but still linear: a runner on the bend of a track, because every part of the body still moves the same distance in the same direction at the same time
- If there is rotation about an axis, it is angular motion, not linear motion
Scalar and vector quantities
A scalar quantity has size (magnitude) only. A vector quantity has both size and direction. Cambridge expects you to sort the biomechanical quantities into the two groups, and to use direction in your answers when the quantity is a vector.
The practical consequence: if the question asks for velocity, an answer without a direction is incomplete in the same way that an answer without a unit is incomplete.
| Quantity | Scalar or vector | Why |
|---|---|---|
| Distance | Scalar | Only how far you have travelled; no direction is needed |
| Displacement | Vector | How far you are from the start point, in a stated direction |
| Speed | Scalar | How fast you are moving; no direction needed |
| Velocity | Vector | How fast you are moving in a stated direction |
| Acceleration | Vector | Rate of change of velocity, which has a direction (slowing down is deceleration) |
| Momentum | Vector | Mass multiplied by velocity, so it carries the direction of the velocity |
| Mass | Scalar | The amount of matter in the body; no direction |
| Time | Scalar | Measured as a duration only |
Distance and displacement
Distance is the total length of the path covered. Displacement is the straight-line distance and direction from the start point to the finish point.
They only match when the path is perfectly straight and in one direction. Change direction and displacement drops below distance.
The hardest version of this is a track and field athlete completing one lap of a 400 m track. The distance covered is 400 m. The displacement is zero, because the athlete finishes at the starting point.
| Situation | Distance | Displacement |
|---|---|---|
| Competitive swimmer completes a 50 m length | 50 m | 50 m (from the starting block to the far wall) |
| Competitive swimmer swims 50 m out and 50 m back | 100 m | 0 m (back at the starting wall) |
| Track and field athlete runs one 400 m lap | 400 m | 0 m (starting point and finishing point are the same) |
| Association football player makes a 30 m run down the wing and cuts inside 10 m | 40 m | Approximately 32 m, diagonally from their start position |
Speed and velocity, with worked calculations
Speed is how fast a body is moving. Velocity is speed in a stated direction. Both are calculated as distance or displacement divided by time.
speed = distance ÷ time
velocity = displacement ÷ time
Worked example 1. A track and field athlete runs 100 m in 10.5 s. Average speed = 100 ÷ 10.5 = 9.5 m/s.
Worked example 2. The same athlete runs one 400 m lap in 50 s. Average speed = 400 ÷ 50 = 8 m/s, but average velocity = 0 ÷ 50 = 0 m/s, because the displacement is zero. Same run, different answer, and the only difference is whether the quantity is a scalar or a vector.
- Average speed uses total distance; instantaneous speed is the speed at one moment (what a speed gun measures).
- Convert units before calculating: 400 m in 1 minute 20 s is 400 ÷ 80.
- Always give the unit. m/s is the standard for both speed and velocity.
Acceleration, with worked calculations
Acceleration is the rate of change of velocity. It happens when a body speeds up, slows down or changes direction.
acceleration = (final velocity − initial velocity) ÷ time taken
Worked example 1. A rugby union player accelerates from 2 m/s to 8 m/s in 2 s. Acceleration = (8 − 2) ÷ 2 = 6 ÷ 2 = 3 m/s².
Worked example 2. A netball player landing after a jump slows from 5 m/s to 0 m/s in 0.5 s. Acceleration = (0 − 5) ÷ 0.5 = −10 m/s². The negative sign means deceleration — the velocity and the acceleration act in opposite directions.
Worked example 3. A competitive swimmer pushes off the wall at 3 m/s and reaches 1 m/s in 1.5 s. Acceleration = (1 − 3) ÷ 1.5 = −1.33 m/s², so they are decelerating through the water.
Momentum
Momentum is the quantity of motion a body has. It is mass multiplied by velocity.
momentum = mass × velocity
Momentum is measured in kg m/s (or newton seconds, N s, which is the same thing). Because velocity is a vector, momentum is a vector too — a change of direction changes the momentum even if the speed stays the same.
Worked example 1. A rugby union player of mass 95 kg runs at 7 m/s. Momentum = 95 × 7 = 665 kg m/s.
Worked example 2. A second player of mass 75 kg runs at 9 m/s. Momentum = 75 × 9 = 675 kg m/s. The lighter player has more momentum because they are travelling faster, which is why size alone does not decide who wins a collision.
- Doubling the velocity doubles the momentum; doubling the mass also doubles it.
- A performer who is stationary has zero momentum however large their mass.
- Momentum is the link between linear motion and Newton's laws — the second law describes the rate of change of momentum.
Graphs of linear motion
Cambridge asks you to draw and interpret graphs of distance, displacement, speed, velocity and time. Read the axes first, then the shape.
On a distance-time graph the gradient is speed, and the line can never go down because distance only ever increases. On a displacement-time graph the line can go down, because displacement falls when the performer turns back towards the start.
On a speed-time graph the gradient is acceleration and the area under the line is the distance travelled. On a velocity-time graph the gradient is acceleration and the area under the line is the displacement.
- A horizontal line on a speed-time graph means constant speed, so acceleration is zero — not that the performer has stopped.
- A horizontal line on a distance-time graph means the performer is stationary.
- The steeper the gradient on a velocity-time graph, the greater the acceleration.
| Graph | What the gradient tells you | What the area under the line tells you | Shape to expect |
|---|---|---|---|
| Distance-time | Speed | Nothing meaningful | Always flat or rising, never falling |
| Displacement-time | Velocity | Nothing meaningful | Can rise and fall as the performer changes direction |
| Speed-time | Acceleration | Distance travelled | Rises during acceleration, flat at constant speed, falls when slowing |
| Velocity-time | Acceleration | Displacement | Can pass below the axis if the performer travels back past the start |
Key terms you must be able to define
- Linear motion
- Movement of a body in a straight or curved line where all parts move the same distance in the same direction over the same time, created by an external force passing through the centre of mass.
- Scalar quantity
- A quantity that has magnitude (size) only, such as distance, speed, mass and time.
- Vector quantity
- A quantity that has both magnitude and direction, such as displacement, velocity, acceleration and momentum.
- Distance
- The total length of the path covered; a scalar quantity.
- Displacement
- The straight-line distance and direction from the start point to the finish point; a vector quantity.
- Speed
- How fast a body is moving, calculated as distance divided by time; a scalar quantity.
- Velocity
- Speed in a stated direction, calculated as displacement divided by time; a vector quantity.
- Acceleration
- The rate of change of velocity, calculated as (final velocity − initial velocity) divided by time taken; measured in m/s².
- Momentum
- The quantity of motion of a body, calculated as mass × velocity; measured in kg m/s.
- Deceleration
- Negative acceleration: a change in velocity in the opposite direction to the motion, so the body slows down.
Applied to your sport
Cambridge requires you to apply this knowledge to physical activities. Use these as models, then write your own for the sport you play.
A 100 m sprinter is in linear motion on the straight: every part of the body moves the same distance in the same direction in the same time, driven by the external force from the blocks and the ground passing through the centre of mass.
A swimmer who completes a 50 m length has a distance and a displacement of 50 m. Swim 50 m out and 50 m back and the distance is 100 m while the displacement is 0 m, so the average velocity over the whole swim is zero.
A 95 kg forward running at 7 m/s has a momentum of 665 kg m/s. A 75 kg back running at 9 m/s has 675 kg m/s, so the lighter player carries more momentum into the tackle.
A player landing from a jump slows from 5 m/s to 0 m/s in 0.5 s, an acceleration of −10 m/s². The negative value shows deceleration, which is why a controlled landing takes longer than 0.5 s.
A player who sprints 30 m to close down an opponent has covered a distance of 30 m at an average speed you can calculate from the time taken, but their displacement is measured in a straight line from where they started.
Flashcards
Click a card to flip it. Mark honestly — the tracker uses this.
Exam-style questions
7 questions, 22 marks. Write your answer, then reveal the mark scheme and tick each point you actually made. Answering honestly here is what makes the rest of the site useful.
Mark scheme — tick each point you actually made
Mark scheme — tick each point you actually made
Mark scheme — tick each point you actually made
Mark scheme — tick each point you actually made
Mark scheme — tick each point you actually made
Mark scheme — tick each point you actually made
Mark scheme — tick each point you actually made
Exam technique for this topic
- Write the formula, substitute the numbers, then give the answer with its unit. Cambridge awards the substitution and the unit separately in calculation questions.
- If the question says velocity, include a direction. If it says speed, a direction is not needed.
- In 'compare' questions about distance and displacement, or speed and velocity, always state both sides — one definition alone caps you at half marks.
- When interpreting a graph, quote the numbers from the axes rather than describing the line: a gradient of 8 m/s over 4 s is an acceleration of 2 m/s².
- Remember displacement can be zero while distance is large. Surfacing that point shows you understand vectors.
Why students lose marks here
Where this fits in AS Level PE 8386
This page is one topic of Cambridge AS Level PE 8386. AS Level PE 8386 is the course home: every area and every topic in Cambridge's own order, the papers you sit and what each one tests, and the exam-practice tools. The full topic list, with each topic linked to its revision page, is on the AS Level PE 8386 syllabus page.