What you'll learn
This revision guide covers everything you need to know about motion and forces for Edexcel GCSE Physics. You'll master scalar and vector quantities, interpret distance-time and velocity-time graphs, apply Newton's laws of motion, and calculate forces including weight, friction and momentum. These topics form the foundation of mechanics and appear frequently in both Paper 1 and Paper 2.
Key terms and definitions
Scalar quantity — a quantity with magnitude (size) only, such as distance, speed, mass, temperature or time
Vector quantity — a quantity with both magnitude and direction, such as displacement, velocity, acceleration, force or momentum
Resultant force — the single force that has the same effect as all the forces acting on an object combined
Newton's First Law — an object remains at rest or continues moving at constant velocity unless acted upon by a resultant force
Newton's Second Law — the acceleration of an object is proportional to the resultant force acting on it and inversely proportional to its mass (F = ma)
Newton's Third Law — when two objects interact, they exert equal and opposite forces on each other
Inertia — the tendency of an object to resist changes in its motion; mass is a measure of inertia
Momentum — the product of an object's mass and velocity (p = mv), measured in kg m/s
Core concepts
Distance, displacement, speed and velocity
Distance and displacement are often confused but are fundamentally different. Distance is a scalar that measures how far an object travels along its path. Displacement is a vector measuring the straight-line distance from the starting point to the finishing point, including direction.
Similarly, speed and velocity differ:
- Speed = distance ÷ time (scalar, measured in m/s)
- Velocity = displacement ÷ time (vector, measured in m/s)
Average speed can be calculated from total distance and total time. To find the speed of an object at a specific moment (instantaneous speed), you need measurements over a very short time interval.
Typical speeds you should know:
- Walking: approximately 1.5 m/s
- Running: approximately 3 m/s
- Cycling: approximately 6 m/s
- Car in town: approximately 13 m/s (30 mph)
- Train: approximately 50 m/s
- Sound in air: approximately 330 m/s
Acceleration
Acceleration is the rate of change of velocity, measured in m/s². It is a vector quantity.
acceleration = change in velocity ÷ time taken
a = (v - u) ÷ t
where:
- a = acceleration (m/s²)
- v = final velocity (m/s)
- u = initial velocity (m/s)
- t = time (s)
Deceleration (negative acceleration) occurs when an object slows down. The magnitude is the same but the direction is opposite to the velocity.
Uniform acceleration means constant acceleration. For uniformly accelerated motion:
(final velocity)² - (initial velocity)² = 2 × acceleration × distance
v² - u² = 2as
where s is the distance travelled (m).
Distance-time and velocity-time graphs
Distance-time graphs show how distance changes over time:
- A horizontal line represents a stationary object (zero speed)
- A straight diagonal line represents constant speed
- The gradient (slope) equals the speed
- A steeper gradient means higher speed
- Curved lines indicate changing speed (acceleration or deceleration)
Velocity-time graphs provide more information:
- A horizontal line represents constant velocity (zero acceleration)
- The gradient equals the acceleration
- A positive gradient shows acceleration
- A negative gradient shows deceleration
- The area under the graph equals the distance travelled
For uniform acceleration, the distance travelled can be found from:
- Area of trapezium = ½(u + v) × t
- Or area of rectangle + triangle
Newton's laws of motion and forces
Newton's First Law explains that objects maintain their state of motion unless a resultant force acts. A book resting on a table stays at rest because the forces are balanced. A spacecraft in deep space continues at constant velocity indefinitely because there are no forces acting on it.
Newton's Second Law gives the mathematical relationship between force, mass and acceleration:
resultant force = mass × acceleration
F = ma
where:
- F = force (N)
- m = mass (kg)
- a = acceleration (m/s²)
This means:
- Larger forces produce greater accelerations
- More massive objects accelerate less for the same force
- The direction of acceleration is the same as the direction of the resultant force
Newton's Third Law states that forces always occur in pairs. When you push against a wall, the wall pushes back with an equal force in the opposite direction. When a rocket expels hot gases downward, the gases push the rocket upward with an equal force.
Key characteristics of Newton's Third Law pairs:
- Equal in magnitude
- Opposite in direction
- Same type of force
- Act on different objects
Weight, mass and gravity
Mass and weight are different:
- Mass is the amount of matter in an object (kg), a scalar quantity that remains constant everywhere
- Weight is the gravitational force acting on an object (N), a vector quantity that varies with gravitational field strength
weight = mass × gravitational field strength
W = mg
where:
- W = weight (N)
- m = mass (kg)
- g = gravitational field strength (N/kg)
On Earth, g ≈ 9.8 N/kg (often approximated to 10 N/kg in calculations). On the Moon, g ≈ 1.6 N/kg. A 60 kg person has a mass of 60 kg everywhere, but weighs 600 N on Earth and only 96 N on the Moon.
Forces and motion
Several forces affect moving objects:
Friction opposes motion between surfaces in contact. It:
- Always acts in the opposite direction to motion
- Converts kinetic energy to thermal energy
- Depends on the surfaces and the normal contact force
- Can be reduced by lubrication or smooth surfaces
Air resistance (drag) opposes motion through air. It:
- Increases with speed (squared relationship at high speeds)
- Increases with cross-sectional area
- Depends on the shape (streamlining reduces drag)
Terminal velocity occurs when a falling object reaches constant velocity. As an object falls:
- Initially, weight > air resistance, so it accelerates downward
- As speed increases, air resistance increases
- Eventually, air resistance = weight
- Resultant force = 0, so acceleration = 0
- The object continues at constant terminal velocity
Momentum and collisions
Momentum (p) is defined as:
momentum = mass × velocity
p = mv
where:
- p = momentum (kg m/s)
- m = mass (kg)
- v = velocity (m/s)
Momentum is a vector quantity in the same direction as velocity.
Conservation of momentum states that in a closed system, total momentum before a collision equals total momentum after:
total momentum before = total momentum after
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
This applies to:
- Collisions between objects
- Explosions and separations
- Vehicles crashing or coupling
Changes in momentum create forces:
force = change in momentum ÷ time taken
F = (mv - mu) ÷ t = m(v - u) ÷ t = ma
This explains why:
- Airbags reduce injuries by increasing collision time, reducing force
- Crumple zones work by extending impact time
- Falling onto concrete hurts more than falling onto cushions
Stopping distances
The stopping distance of a vehicle equals:
stopping distance = thinking distance + braking distance
Thinking distance is the distance travelled during the driver's reaction time (before brakes are applied). It increases with:
- Higher speed (directly proportional)
- Slower reactions (tiredness, alcohol, drugs, distractions)
Braking distance is the distance travelled while braking. It increases with:
- Higher speed (proportional to speed squared, from v² = u² + 2as)
- Poor road conditions (wet, icy)
- Poor tyre conditions (worn tread)
- Poor brake conditions (worn pads)
- Heavier vehicles (greater mass)
During braking, work done by friction converts kinetic energy to thermal energy in the brakes:
work done by braking force = kinetic energy lost
F × s = ½mv²
Worked examples
Example 1: Calculating acceleration
Question: A car accelerates from rest to 28 m/s in 8.0 seconds. Calculate the acceleration of the car. (3 marks)
Solution:
- Identify known values: u = 0 m/s (from rest), v = 28 m/s, t = 8.0 s
- Select equation: a = (v - u) ÷ t [1 mark]
- Substitute: a = (28 - 0) ÷ 8.0 [1 mark]
- Calculate: a = 3.5 m/s² [1 mark]
Example 2: Momentum conservation
Question: A 1200 kg car travelling at 15 m/s collides with a stationary 800 kg car. After the collision, the vehicles move together. Calculate their velocity after the collision. (4 marks)
Solution:
- Total momentum before = total momentum after [1 mark]
- Before: p = (1200 × 15) + (800 × 0) = 18,000 kg m/s [1 mark]
- After: p = (1200 + 800) × v = 2000v [1 mark]
- Therefore: 2000v = 18,000, so v = 9.0 m/s [1 mark]
Example 3: Interpreting velocity-time graphs
Question: A velocity-time graph shows a straight line from (0, 0) to (5, 20), then horizontal to (10, 20). Calculate: (a) the acceleration in the first 5 seconds (2 marks), (b) the total distance travelled (3 marks).
Solution:
(a) Acceleration = gradient = (20 - 0) ÷ (5 - 0) [1 mark] = 4 m/s² [1 mark]
(b) Distance = area under graph = area of triangle + area of rectangle = (½ × 5 × 20) + (5 × 20) [1 mark] = 50 + 100 [1 mark] = 150 m [1 mark]
Common mistakes and how to avoid them
Confusing mass and weight — Remember mass is in kg (scalar), weight is in N (vector). Always use W = mg to convert between them.
Forgetting direction in vector calculations — Velocity, momentum and force are vectors. In collision problems, use + and - to indicate opposite directions. A car travelling at -5 m/s means moving in the opposite direction to the positive reference.
Misreading graph gradients — On distance-time graphs, gradient = speed. On velocity-time graphs, gradient = acceleration. Students often confuse these or try to find speed from velocity-time graphs.
Incorrectly applying Newton's Third Law — The equal and opposite forces act on different objects, not on the same object. The weight of a book and the normal contact force from a table are NOT a Newton's Third Law pair because they both act on the book.
Wrong units in calculations — Always convert to standard units: distances to metres, time to seconds, mass to kilograms. A common error is leaving time in minutes or mass in grams.
Misunderstanding terminal velocity — At terminal velocity, forces are balanced (resultant force = 0), NOT zero forces. Weight still acts downward and air resistance acts upward; they're just equal in magnitude.
Exam technique for "Motion and forces"
Command words matter — "Calculate" requires a numerical answer with working and units. "Explain" needs reasons using physics principles. "Describe" requires stating what happens without detailed reasons. "State" needs a brief answer without explanation.
Show all working in calculations — Even if your final answer is wrong, you earn method marks for correct equations, substitution and working. Write the equation, substitute values with units, then calculate. This three-step approach maximises marks.
Use vector notation carefully — In momentum and force questions, establish a positive direction and stick to it. Show negative signs clearly for opposite directions. Draw diagrams with arrows to visualise force or velocity directions.
Graph questions require precision — Use a ruler for gradients and area calculations. Show your method clearly: for area, split complex shapes into triangles and rectangles. For gradient, show two points used and the calculation Δy ÷ Δx.
Quick revision summary
Motion involves scalar quantities (distance, speed) and vector quantities (displacement, velocity, acceleration). Distance-time graphs show speed as gradient; velocity-time graphs show acceleration as gradient and distance as area under the curve. Newton's three laws govern forces and motion: objects maintain motion unless forced to change; F = ma links force, mass and acceleration; forces occur in equal opposite pairs on different objects. Weight (W = mg) differs from mass. Momentum (p = mv) is conserved in collisions. Stopping distance comprises thinking distance plus braking distance, both affected by different factors.