OxfordAQA International GCSE Physics: Momentum, collisions and safety in road transport (9203) – Revision Notes

These notes condense sections 3.1.4 (Momentum, full Physics content marked P) and 3.1.5 (Safety in public transport) of the OxfordAQA International GCSE Physics (9203) specification, for exams May/June 2018 onwards. For full explanations read the study guide, then test yourself with the practice questions.

Related pages: the OxfordAQA International GCSE Physics hub, the printable checklist, the forces overview and the free diagnostics.

Equations

Quantity	Equation	Units
Momentum	p = mv	kg m/s
Force and momentum change	F = Δp / t	N, kg m/s, s
Resultant force	F = ma	N, kg, m/s²
Thinking distance	speed × reaction time	m
Stopping distance	thinking distance + braking distance	m
Work done by brakes	force × distance, equal to the kinetic energy lost	J
Kinetic energy	½mv²	J

3.1.4 a: momentum

• All moving objects have momentum, and it has a direction.
• Choose one direction as positive; opposite direction is negative.
• Doubling the mass or doubling the velocity doubles the momentum.

3.1.4 b: conservation of momentum

Definition: in a closed system, adding up the momentum of every object gives the same total before and after they interact.

Method in steps:

1. Sketch before and after, and choose a positive direction.
2. Write total momentum before: add each mass × velocity, with signs.
3. Write total momentum after in the same way.
4. Set before equal to after and solve for the unknown.
5. Check the sign and direction of your answer.

Collision, objects stick together. A 0.40 kg trolley at 2.5 m/s hits a stationary 0.10 kg trolley and they join. Before: 0.40 × 2.5 = 1.0 kg m/s. After: (0.40 + 0.10) × v = 0.50v. So v = 2.0 m/s.

Explosion. Two skaters stand at rest on ice and push apart. The 70 kg skater moves right at 1.5 m/s. Momentum of 70 kg skater = 70 × 1.5 = 105 kg m/s right. The 50 kg skater must have 105 kg m/s left, so v = 105 / 50 = 2.1 m/s left.

Key facts for explosions:

• Total momentum before is zero (starting at rest), so total after is zero.
• The momenta are equal in size and opposite in direction.
• The lighter object gets the higher speed.

3.1.4 c: F = Δp / t

• Force is the momentum change divided by the time taken.
• For the same change of momentum, a longer time means a smaller force.
• Write Δp as mass × change in velocity. If an object rebounds, the velocity changes sign, so add the two speeds.

Worked reminder. A 60 kg passenger travelling at 10 m/s is stopped by a seat belt in 0.25 s. Δp = 60 × 10 = 600 kg m/s. F = 600 / 0.25 = 2400 N. If the same passenger stopped in 0.020 s against a hard surface, F = 600 / 0.020 = 30 000 N.

Safety features: one-line explanations

Feature	Key point
Air bag	Increases stopping time and area of contact, so force and pressure on the body are smaller
Seat belt	Stretches, so stopping time is longer; stops you hitting the windscreen
Crumple zone	Collapses in a controlled way, increasing the time for the car to stop
Side impact bar	Spreads the force of a side hit through the car body and keeps the door from being pushed in
Crash mat	Compresses, so the gymnast stops over a longer time
Playground surface	Soft, so the child stops over a longer time than on concrete
Cycle helmet	Foam crushes, so the head stops over a longer time

Model sentence for any of these: “The feature increases the time taken to change the momentum to zero, so the rate of change of momentum is smaller, so the force on the person is smaller.”

3.1.5 a: steady speed

• Steady speed in a straight line means the resultant force is zero.
• Driving force = resistive forces, opposite in direction.
• If driving force becomes greater than the resistive forces, the vehicle accelerates. If it becomes smaller, the vehicle decelerates.

3.1.5 b: speed, braking force and deceleration

• Bigger braking force means bigger deceleration (a = F / m).
• Greater speed needs a bigger braking force to stop in the same distance.
• For a fixed braking force, a greater speed gives a greater stopping distance.
• Very large decelerations can cause brake overheating and loss of control.

3.1.5 c: stopping distance

Stopping distance = thinking distance + braking distance.

Distance	Depends on
Thinking	Speed and reaction time
Braking	Speed, braking force (road and vehicle condition) and mass

Reaction time is made longer by:

• tiredness
• distractions
• drugs
• alcohol

A longer reaction time changes thinking distance only.

3.1.5 d: brakes and energy

• Friction between the brake and the wheel does work.
• This reduces the kinetic energy of the vehicle.
• The energy transferred raises the temperature of the brakes.
• Braking force × braking distance = kinetic energy lost.

Worked reminder. A 900 kg car at 12 m/s, reaction time 0.90 s, braking force 4000 N. Thinking distance = 12 × 0.90 = 10.8 m. Kinetic energy = ½ × 900 × 12² = 64 800 J. Braking distance = 64 800 / 4000 = 16.2 m. Stopping distance = 10.8 + 16.2 = 27.0 m. Deceleration = 4000 / 900 = 4.4 m/s² (2 significant figures).

Speed doubling. Kinetic energy is proportional to speed squared. At twice the speed, the same car at 24 m/s has four times the kinetic energy (259 200 J), so for the same braking force the braking distance is four times as long (64.8 m). Thinking distance only doubles.

3.1.5 e: adverse conditions and vehicle condition

Condition	Effect on braking
Wet road	Less friction, smaller braking force, longer braking distance
Icy road	Much less friction, much longer braking distance
Worn tyres	Less grip, so tyres can skid sooner; longer braking distance
Worn brakes	Less friction force from brake pads; longer braking distance

Poor condition of the car is limited to its brakes or tyres in this specification.

Must-know distinctions

• Thinking distance (driver) vs braking distance (vehicle and road).
• Momentum (vector, kg m/s) vs kinetic energy (scalar, J).
• Change in momentum (same with or without a safety feature) vs force (smaller with the safety feature).
• Balanced forces at steady speed vs no forces: the vehicle still has driving and resistive forces.

Quick self-test

1. Find the momentum of a 1200 kg van moving at 15 m/s.
2. A 4.0 kg trolley at 1.5 m/s hits a stationary 2.0 kg trolley and they stick. Find their velocity.
3. A 3.0 kg gun at rest fires a 0.030 kg bullet at 200 m/s. Find the recoil speed of the gun.
4. A ball of mass 0.20 kg changes its momentum by 3.0 kg m/s in 0.050 s. Find the force.
5. Explain why a crumple zone reduces injury.
6. A car travels at a steady speed with a driving force of 900 N. State the size of the resistive forces.
7. A driver at 25 m/s has a reaction time of 0.80 s. Find the thinking distance.
8. State two factors that increase a driver’s reaction time.
9. A car has kinetic energy 150 000 J and is stopped by a braking force of 6000 N. Find the braking distance.
10. State what happens to the braking distance when speed doubles and the braking force stays the same.
11. Why do wet roads increase braking distance?

Answers

1. p = 1200 × 15 = 18 000 kg m/s.
2. Before: 4.0 × 1.5 = 6.0. After: 6.0v. So v = 1.0 m/s.
3. Momentum of bullet = 0.030 × 200 = 6.0 kg m/s. Gun has equal momentum backwards: v = 6.0 / 3.0 = 2.0 m/s.
4. F = 3.0 / 0.050 = 60 N.
5. It collapses and increases the time for the car to stop. The momentum changes more slowly, so the force on the passengers is smaller.
6. 900 N, in the opposite direction.
7. 25 × 0.80 = 20 m.
8. Any two of tiredness, distractions, drugs, alcohol.
9. 150 000 / 6000 = 25 m.
10. It becomes four times as long.
11. Less friction between tyre and road, so the maximum braking force is smaller.

Where marks are usually lost

• Leaving out the unit, or writing kg m/s for a force.
• Ignoring the direction of velocity when objects move towards each other.
• Using only the mass of one object after objects stick together.
• Saying “the time is longer so the force is less” without linking to the change of momentum.
• Describing a seat belt only as “holding you in” and ignoring stopping time.
• Putting tiredness or alcohol under braking distance.
• Doubling the braking distance when speed doubles.
• Saying brakes “use up” energy, rather than transferring kinetic energy to thermal energy.

Official syllabus

OxfordAQA International GCSE Physics (9203) specification, for exams May/June 2018 onwards, published by OxfordAQA.