Linear motion — AQA A-Level Physical Education

Linear motion is a fundamental topic in AQA A-Level Physical Education, focusing on the biomechanics of movement along a straight or curved path. It covers scalar and vector quantities, displacement, velocity, acceleration, and the equations of uniformly accelerated motion. Understanding these concepts allows students to analyse and improve performance in activities such as sprinting, swimming, and cycling.

This topic is essential for the biomechanical analysis section of the specification and provides the mathematical foundation for more complex motion, including projectile motion and angular motion. It also links to Newton's laws of motion and the application of forces, helping students explain how athletes generate speed, decelerate efficiently, and optimise technique.

• →Scalar quantities (distance, speed) have magnitude only, while vector quantities (displacement, velocity, acceleration) have both magnitude and direction.
• →Displacement is the straight-line distance from start to finish in a specified direction; distance is the total path length covered.
• →Velocity is the rate of change of displacement (v = s/t), and acceleration is the rate of change of velocity (a = (v - u)/t).
• →The equations of uniformly accelerated motion (v = u + at, s = ut + 0.5at^2, v^2 = u^2 + 2as, s = ((u + v)/2)t) are used to solve problems involving constant acceleration.
• →In linear motion, all body parts move the same distance, in the same direction, at the same speed, which is rare in sport but approximated in straight-line sprinting or cycling.

• Weight is the gravitational force on the performer, acting vertically downwards through the centre of mass.
• Frictional force acts along the contact surface and opposes the relative sliding tendency between shoe and ground.
• Air resistance (drag) acts in the direction opposite to the performer's motion through the air.
• Internal-muscular force is produced by the performer's own muscles and provides propulsion; it is internal to the body but still drives the motion.
• A free-body diagram represents the performer as a point with labelled force arrows, allowing net force to be found by vector addition.
• Net force determines acceleration, so identifying the direction and relative size of each force explains speeding up, slowing down or steady speed.
• Gravity is the attractive force between masses and produces a gravitational field strength of about 9.81 N kg⁻¹ near the Earth's surface.
• Weight is the gravitational force acting on a performer, calculated as mass multiplied by gravitational field strength, and acts vertically downwards through the centre of mass.
• Frictional force acts at the contact surface between shoe and ground, opposing the relative sliding tendency; static friction enables grip and push-off.
• Air resistance is a drag force opposing motion through the air, increasing with speed and frontal area.
• Internal-muscular force is generated by muscle contraction inside the performer and drives propulsion when transmitted to the ground.
• Weight and gravity are related but not identical terms: gravity is the interaction, weight is the force experienced by a particular mass.
• Defines a vector as a quantity with magnitude and direction, and a scalar as magnitude only.
• Identifies displacement, velocity, acceleration, weight and momentum as vectors in linear motion.
• States the equation velocity = displacement ÷ time with consistent units.
• States the equation acceleration = change in velocity ÷ time with consistent units.
• States the equation weight = mass × gravitational field strength and gives weight in newtons.
• States the equation momentum = mass × velocity and gives momentum in kg m s⁻¹.
• Uses correct units: m, m s⁻¹, m s⁻², N and kg m s⁻¹, with direction where required.
• Defines weight as the force of gravity on a mass and gives W = m × g in newtons.
• Defines velocity as rate of change of displacement and gives v = s ÷ t in m s⁻¹ with direction.
• Defines displacement as distance in a stated direction and gives the unit m.
• Defines acceleration as rate of change of velocity and gives a = Δv ÷ t in m s⁻².
• Defines momentum as mass × velocity and gives p = m × v in kg m s⁻¹.
• Classifies all five quantities as vectors and includes direction in answers.
• Applies the equations to numerical data with correct substitution and units.
• A scalar is fully described by magnitude alone and requires no direction.
• Mass is a scalar measured in kilograms (kg), representing the quantity of matter.
• Inertia is a scalar representing a body's resistance to a change in its state of motion.
• Distance is a scalar measured in metres (m), representing the total path length.
• Speed is a scalar measured in metres per second (m s⁻¹), calculated as distance ÷ time.
• Unit conversions: 1 kg = 1000 g, so divide grams by 1000; 1 minute = 60 s, so multiply minutes by 60.
• Mass is the quantity of matter in a body and is measured in kilograms (kg).
• Distance is the total length of the path travelled and is measured in metres (m).
• Speed is the rate of change of distance and is measured in metres per second (m s⁻¹).
• Mass, speed and distance are scalars, meaning magnitude alone defines them without a specific direction.
• Speed = distance ÷ time.
• Average speed is total distance divided by total time, for example 400 m ÷ 50 s = 8 m s⁻¹.
• Mass is unaffected by gravitational field strength, unlike weight, which is a force in newtons (N).
• Impulse is defined as force multiplied by the time for which the force acts, and it equals the change in momentum.
• On a force/time graph, impulse is represented by the area between the force curve and the time axis.
• A positive area (force in the direction of motion) increases forward momentum during sprinting.
• A negative area (force opposing motion, such as during braking) decreases forward momentum.
• The net impulse is the algebraic sum of positive and negative areas, giving the overall change in momentum.
• Students should calculate areas by dividing the graph into rectangles and triangles and using appropriate units (N s or kg m s⁻¹).

• 💡Read the stem carefully to identify which single force the question targets, then eliminate options that describe a different force or the wrong direction.
• 💡Check the direction wording in each option: weight is always vertically downwards, friction opposes sliding along the surface, and drag opposes motion through the air.
• 💡Where a diagram is given, confirm the arrow's point of application and direction before choosing, because a correct force drawn in the wrong direction is still wrong.
• 💡Match each option to the force definition before choosing, because distractors often swap the origin or direction of two forces.
• 💡Check units in any numerical option: weight must be in newtons, mass in kilograms, and gravitational field strength in N kg⁻¹.
• 💡For friction questions, decide first whether the contact is sliding or gripping, since that determines whether friction opposes motion or enables it.
• 💡In multiple-choice questions, eliminate options that give a scalar unit for a vector quantity or omit direction.
• 💡Check that every equation you use has matching units before substituting numbers.
• 💡When a question asks for velocity, acceleration, weight or momentum, include both the numerical value with its unit and the direction if the quantity is a vector.
• 💡Underline the quantity asked for in the question and match it to the correct equation and unit.
• 💡For vector quantities, check that your answer includes a direction such as north, south, left or right.
• 💡In multiple-choice questions, reject options that use the wrong unit, for example N for momentum or kg for weight.
• 💡Underline the quantity the question asks you to find, then select the matching equation before substituting numbers.
• 💡Convert all values to kg, m and s before calculating, then write the unit after your answer.
• 💡Check whether the option is a scalar or a vector by asking whether a direction is needed to define it fully.
• 💡Read the option carefully to check whether it describes a scalar or a vector before selecting it.
• 💡When a calculation is involved, write the equation speed = distance ÷ time, substitute the values with units, then state the answer in m s⁻¹.
• 💡For average speed, use total distance and total time, not the speed at a single instant.
• 💡Always state that impulse is the area under a force/time graph, and show your method for calculating that area.
• 💡When a graph has sections above and below the axis, calculate each area separately and then find the net area by subtraction.
• 💡Use the correct units: force in newtons, time in seconds, impulse in newton seconds (N s) or kilogram metres per second (kg m s⁻¹).
• 💡Link your answer back to sprinting by explaining how the net impulse changes the sprinter's forward momentum.
• 💡Always show your working and include units in your final answer. Marks are awarded for correct substitution and clear steps, not just the final value.
• 💡When answering longer questions, use correct terminology such as 'displacement', 'velocity', and 'acceleration' rather than 'distance' and 'speed' when direction is involved.
• 💡For graph questions, remember that the gradient of a displacement-time graph gives velocity, and the gradient of a velocity-time graph gives acceleration. The area under a velocity-time graph gives displacement.

• Treating weight and normal reaction as an equal-and-opposite pair in every situation: they are only equal in magnitude when the surface is horizontal and there is no vertical acceleration, so on a slope the normal reaction is smaller than weight.
• Drawing internal-muscular force as an external arrow acting on the performer from outside: it is generated within the body, so it is shown as the force the performer exerts on the ground, with the ground's reaction propelling the body forward.
• Assuming air resistance is negligible at all speeds: it grows with speed and frontal area, so it becomes significant in sprinting, cycling and downhill running.
• Confusing mass with weight: mass is measured in kilograms and is constant, whereas weight is a force measured in newtons and equals mass multiplied by gravitational field strength.
• Using weight and gravity as exact synonyms: gravity is the interaction between masses, while weight is the force that interaction produces on a specific mass.
• Giving weight in kilograms: weight is a force measured in newtons, so a 70 kg performer has a weight of about 687 N, not 70 N.
• Describing friction as always opposing motion: static friction at the shoe can act forwards, in the direction of travel, to propel the performer.
• Treating air resistance as constant: it rises with speed and frontal area, so it matters far more in cycling or sprinting than in a slow walk.
• Treating speed as a vector: speed is a scalar with magnitude only, whereas velocity is a vector and needs a stated direction.
• Confusing mass and weight: mass is a scalar measured in kilograms, while weight is a vector force measured in newtons and calculated as W = m × g.
• Omitting direction from a vector answer: a velocity of 5 m s⁻¹ is incomplete; write 5 m s⁻¹ north or another stated direction.
• Using the wrong unit for momentum: momentum is measured in kg m s⁻¹, not N or J.
• Confusing weight with mass: weight is a force in newtons, while mass is a scalar in kilograms.
• Treating displacement as total distance travelled: displacement is the straight-line distance in a stated direction from start to finish.
• Forgetting that acceleration can be negative when velocity decreases, and omitting the direction or sign.
• Calculating momentum without direction: momentum is a vector, so a value such as 210 kg m s⁻¹ needs a stated direction.
• Treating speed as a vector: speed has magnitude only, whereas velocity includes direction, so a car travelling at 20 m s⁻¹ has that speed regardless of its heading.
• Confusing mass with weight: mass is a scalar in kg, while weight is a force in newtons (N) equal to mass × gravitational field strength.
• Using inconsistent units, such as dividing metres by minutes: convert time to seconds first so the answer is in m s⁻¹.
• Omitting the unit from the final answer: a numerical value without its unit is incomplete in linear motion calculations.
• Confusing distance with displacement: distance is the total path length, whereas displacement is the straight-line distance in a stated direction, so a 400 m lap finishing at the start has a displacement of 0 m.
• Confusing mass with weight: mass in kg is a scalar, while weight in N is a force equal to mass × gravitational field strength.
• Using the wrong unit for speed, such as m: speed is m s⁻¹ because it is distance in metres divided by time in seconds.
• Assuming speed must include direction: speed is a scalar, so a value such as 8 m s⁻¹ is complete without a direction.
• Misunderstanding: the gradient of a force/time graph gives impulse. Correction: the gradient gives the rate of change of force, while the area under the graph gives impulse.
• Misunderstanding: any area under a force/time graph increases momentum. Correction: areas below the time axis represent negative impulse and decrease momentum.
• Misunderstanding: impulse and momentum are unrelated quantities. Correction: impulse equals the change in momentum, so a net impulse of 20 N s produces a momentum change of 20 kg m s⁻¹.
• Misunderstanding: a short contact time cannot produce a large impulse. Correction: a large force over a short time can produce a large impulse, as in a sprint start.
• Students often think that if an object returns to its starting point, its displacement and velocity are non-zero. In fact, displacement is zero, so average velocity is zero, even though distance and speed are not.
• Many students forget that acceleration can be negative (deceleration) and that the sign indicates direction relative to the chosen positive direction. Always define a positive direction before solving.
• Some students assume that a constant speed means zero acceleration. However, if direction changes, velocity changes, so acceleration is non-zero (e.g., circular motion at constant speed).

1. 1Day 1-2: Learn definitions of scalar and vector quantities, distance vs displacement, speed vs velocity, and acceleration. Create flashcards with examples from sport.
2. 2Day 3-4: Memorise the four equations of uniformly accelerated motion and practise rearranging them. Complete basic calculation problems with unit conversions.
3. 3Day 5-6: Apply the equations to sporting scenarios such as sprint starts, braking distances, and projectile motion. Draw motion graphs and interpret gradients and areas.
4. 4Day 7-8: Attempt exam-style questions, focusing on structured 6-mark answers. Review mark schemes to understand how marks are awarded for method and accuracy.
5. 5Day 9-10: Complete a timed past paper question on linear motion, then self-assess using the mark scheme. Revise any weak areas and repeat active recall prompts.

• 📋Multiple-choice questions testing definitions and distinctions between scalar and vector quantities, or simple calculations of speed, velocity, and acceleration.
• 📋Short-answer calculations (2-4 marks) requiring use of equations of motion, often with unit conversions. Advice: write down the equation, substitute values with units, and give the answer with correct units and direction if vector.
• 📋Structured 6-mark questions analysing a sporting movement, requiring explanation of displacement, velocity, and acceleration, and application to performance. Advice: use specific sporting examples, correct terminology, and link to technique or safety.
• 📋Graph interpretation questions (4-6 marks) where students must calculate velocity from a displacement-time graph or acceleration from a velocity-time graph, and describe motion. Advice: state the formula, show calculation, and describe the motion in words.