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.

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.

Speed or 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:

You should know the order of magnitude of everyday speeds, because exam questions expect sensible estimates:

Acceleration

If velocity changes, the object accelerates (speeds up) or decelerates (slows down). Acceleration is the change in velocity each second:

Free-fall acceleration due to gravity on Earth is about g = 10 m/s² (a skydiver at first speeds up by about 10 m/s every second; as air resistance grows, the acceleration gets smaller).

If the velocity is positive, a negative acceleration means the object is slowing down (decelerating) — the velocity is still changing, just in the opposite sense.

Your turn — acceleration

Distance–time graphs

On a distance–time graph, time is on the x-axis and distance on the y-axis, so the gradient = speed:

Velocity–time graphs

On a velocity–time graph the gradient = acceleration, and the area under the line = 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.

Reading a velocity–time graph

How can one line tell the whole journey?

Uniform acceleration equation

When acceleration is uniform (constant), this equation links velocities, acceleration and distance — without needing the time:

With v = 0 and the same braking force, it gives braking distance ∝ speed²: double the speed and the distance needed to stop quadruples — a key safety idea you'll meet in 4.3.

Your turn — v² = u² + 2ax

Same push: why do the trolleys differ?

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.

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.

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:

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.

Your turn — F = ma

Same push: why do the trolleys differ?

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.

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.

Spotting a Newton pair

What pushes the cannon backwards?

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:

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.

Your turn — 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:

Your turn — conservation of momentum

What pushes the cannon backwards?

Force = rate of change of momentum

Newton's second law can be written in terms of momentum (this equation is not on the Eduqas equation list, but it follows from F = ma with a = Δv ÷ t). The resultant force equals how fast the momentum changes:

This is the key to vehicle safety: for a given change in momentum, spreading the change over a longer time means a smaller force.

Your turn — F = Δp ÷ t (Higher)

Why does a distracted driver stop later?

Stopping distance

The total stopping distance of a vehicle is made of two parts:

• Thinking distance grows with speed and a longer reaction time (typically 0.2–0.9 s; measure it with a ruler-drop test) — increased by tiredness, distraction, alcohol or drugs.
• Braking distance grows with speed (∝ speed² for the same braking force) and with poor conditions: wet/icy roads, worn tyres or brakes, and a heavier loaded vehicle.

Thinking or braking distance?

Tap the part of the stopping distance that each factor mainly affects.

Why does a distracted driver stop later?

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.

• 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.

Explaining a safety feature

The equations to know

You've covered the key ideas across the 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.