This mini-lesson walks you through the whole of Eduqas Topic 4 — Forces and motion: how we describe motion with speed, velocity and acceleration and motion graphs, how Newton's three laws and momentum link forces to motion, and how those ideas keep us safe in vehicles.
Work through each screen, answer the questions as you go (some are wordy, some are calculations) and collect ⭐ stars. Higher-tier-only ideas are clearly flagged. Press Start when you're ready.
4.1 · Scalars and vectors
Distance vs displacement
Distance is how far an object has moved — a scalar (size only). Displacement is the straight-line distance and direction from start to finish — a vector.
Run one full lap of a track and your distance is the whole loop, but your displacement is zero — you finished where you started.
Watch out:velocity is a vector — it always carries a direction. Two cars travelling at 30 m/s in opposite directions have the same speed but different velocities. A sign (+ or −) shows the direction.
Quick check
Speed or velocity?
?A satellite orbits Earth at a steady 7 700 m/s. Its speed is constant, yet physicists say its velocity is constantly changing. Why?
4.1 · Speed and velocity
Speed and typical values
Speed is how fast something travels; velocity is speed in a stated direction. Both use the same relationship to distance (or displacement) and time:
v = x ÷ tspeed/velocity (m/s) = distance or displacement (m) ÷ time (s)
You should know the order of magnitude of everyday speeds, because exam questions expect sensible estimates:
Typical speeds (m/s). The walking wind speed across the UK averages about 4.5 m/s.
Worked example
A cyclist covers 90 m in 15 s.
v = x ÷ t = 90 ÷ 15 = 6 m/s
4.1 · Acceleration
Acceleration
If velocity changes, the object accelerates (speeds up) or decelerates (slows down). Acceleration is the change in velocity each second:
a = Δv ÷ t = (v − u) ÷ tacceleration (m/s²) = change in velocity (m/s) ÷ time (s) u = initial velocity, v = final velocity
Free-fall acceleration due to gravity on Earth is about g = 10 m/s² (a skydiver speeds up by 10 m/s every second until air resistance grows).
Worked example
A car speeds up from 8 m/s to 20 m/s in 6 s.
a = (v − u) ÷ t = (20 − 8) ÷ 6 = 12 ÷ 6 = 2 m/s²
A negative acceleration means the object is slowing down (decelerating) — the velocity is still changing, just in the opposite sense.
Calculate
Your turn — acceleration
1A train pulls away from a station, reaching 24 m/s from rest in 8 s. Calculate its acceleration.
m/s²
Hint: a = (v − u) ÷ t = (24 − 0) ÷ 8.
4.1 · Motion graphs
Distance–time graphs
On a distance–time graph, time is on the x-axis and distance on the y-axis, so the gradient = velocity:
Steeper gradient → faster. A horizontal line means the object is stationary. A curve means the velocity is changing (accelerating); take a tangent to find the velocity at an instant.4.1 · Motion graphs
Velocity–time graphs
On a velocity–time graph the gradient = acceleration, and the area under the line = distance travelled:
A rising line is acceleration; a flat line is constant velocity; a falling line is deceleration. The shaded area under the whole line gives the total distance travelled.
Watch out: on a distance–time graph the gradient is velocity; on a velocity–time graph the gradient is acceleration and the area is distance. Mixing them up is the classic exam slip.
Quick check
Reading a velocity–time graph
?On a velocity–time graph, a line slopes steadily upward and then becomes horizontal. What does the horizontal part show?
4.1 · Equation of motion
Uniform acceleration equation
When acceleration is uniform (constant), this equation links velocities, acceleration and distance — without needing the time:
v² = u² + 2 a xv = final velocity (m/s), u = initial velocity (m/s), a = acceleration (m/s²), x = distance (m)
Worked example
A car starts from rest (u = 0) and accelerates at 2 m/s² over 25 m. Find its final velocity.
v² = u² + 2ax = 0 + 2 × 2 × 25 = 100
v = √100 = 10 m/s
Rearranged, this gives braking distance ∝ speed²: double the speed and the distance needed to stop quadruples — a key safety idea you'll meet in 4.3.
Calculate
Your turn — v² = u² + 2ax
2A motorbike accelerates uniformly from rest at 2 m/s² over a distance of 25 m. Calculate its final velocity.
m/s
Hint: v² = 0 + 2 × 2 × 25 = 100, then v = √100.
4.2 · Newton's first law
Newton's first law & inertia
A body stays at rest, or keeps moving at constant velocity in a straight line, unless acted on by a resultant force.
So if the forces on an object are balanced (no resultant force), its motion does not change. Inertia is this tendency to resist a change in motion; the greater the mass, the greater the inertia.
When thrust = drag, the resultant force is zero — the car keeps a constant velocity, it does not slow down.
Watch out: balanced forces do not always mean "at rest". They mean no change in motion — a stationary object stays still and a moving one keeps the same velocity.
4.2 · Newton's second law
Newton's second law: F = ma
A resultant force changes an object's velocity — it causes acceleration. The acceleration depends on the force and the mass:
F = m aresultant force (N) = mass (kg) × acceleration (m/s²)
The bigger the resultant force, the greater the acceleration; the bigger the mass, the smaller the acceleration. Mass measured this way — its resistance to acceleration — is the object's inertial mass.
Worked example
A resultant force of 1500 N acts on a 600 kg dragster.
a = F ÷ m = 1500 ÷ 600 = 2.5 m/s²
Calculate
Your turn — F = ma
3A 1200 kg car accelerates at 2.5 m/s². Calculate the resultant force driving it forward.
N
Hint: F = m × a = 1200 × 2.5.
4.2 · Newton's third law
Newton's third law
When two objects interact, they exert equal and opposite forces on each other.
The two forces of a "Newton pair" are the same size, opposite in direction, the same type, and crucially they act on different objects.
Jump from a boat and you push the boat backwards; the boat pushes you forwards with an equal force. The two forces act on different objects.
Watch out: the two forces in a third-law pair never act on the same object, so they can't "cancel out". If they acted on one object, nothing would ever move.
Quick check
Spotting a Newton pair
?A swimmer pushes backwards on the water and shoots forwards. Which statement about this Newton's-third-law pair is correct?
4.2 · Momentum
Momentum
A moving object has momentum — the harder it is to stop or turn, the more momentum it has. It depends on mass and velocity:
p = m vmomentum (kg m/s) = mass (kg) × velocity (m/s)
Momentum is a vector (it has direction, like velocity). A heavy lorry at low speed can carry as much momentum as a light car at high speed.
Worked example
A 1500 kg car travels at 12 m/s.
p = m × v = 1500 × 12 = 18 000 kg m/s
Calculate
Your turn — momentum
4A 1500 kg car drives along a road at 12 m/s. Calculate its momentum.
kg m/s
Hint: p = m × v = 1500 × 12.
4.2 · Conservation of momentum
Conservation of momentum
In a closed system (no external forces), the total momentum before an event equals the total momentum after — for collisions and explosions:
total p (before) = total p (after)m₁u₁ + m₂u₂ = (m₁ + m₂)v (for objects that stick together)
800 kg × 6 m/s = 4800 kg m/s before. After they join: 4800 = 1200 × v, so v = 4 m/s.Calculate
Your turn — conservation of momentum
5An 800 kg truck moving at 6 m/s collides with a stationary 400 kg truck and they couple together. Calculate their shared velocity afterwards.
Thinking distance is travelled during the driver's reaction time; braking distance is travelled while the brakes slow the car.
Thinking distance grows with speed and a longer reaction time — increased by tiredness, distraction, alcohol or drugs.
Braking distance grows with speed (∝ speed²) and with poor conditions: wet/icy roads, worn tyres or brakes, and a heavier loaded vehicle.
Sort it
Thinking or braking distance?
Tap the part of the stopping distance that each factor mainly affects.
4.3 · Vehicle safety
Why safety features work
In a crash a large change in momentum happens. Safety features all do the same job: they increase the time (and distance) over which a passenger stops, so by F = Δp ÷ t the force is reduced.
The crumple zone deforms on impact, lengthening the stopping time and lowering the force on the people inside.
Crumple zones — fold and deform, extending the time the car takes to stop.
Seatbelts — stretch slightly, increasing the distance and time over which you stop.
Air bags — inflate so your head decelerates over a longer time against the bag.
Watch out: these features don't reduce the change in momentum — that's fixed by your mass and speed. They reduce the force by making the stop take longer.
Quick check
Explaining a safety feature
?An air bag inflates in a crash. Using physics, why does this reduce the chance of injury?
Recap
The equations to know
Speed/velocity: v = x ÷ t
Acceleration: a = Δv ÷ t = (v − u) ÷ t
Uniform acceleration: v² = u² + 2 a x
Newton's second law: F = m a
Momentum: p = m v (conserved in a closed system)
Force & momentum (Higher): F = Δp ÷ t
You've covered all three parts of Eduqas Topic 4 — speed, velocity, acceleration & motion graphs; forces, accelerations & Newton's laws; and safety in public transport. Press Finish to see your score.
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