Forces, motion and stopping distances

Newton's first and second laws

Newton's first law: a body continues at rest or constant velocity unless a resultant force acts on it. A non-zero resultant force causes acceleration.

Newton's second law: F = m × a. Units: F in newtons (N), m in kg, a in m/s².

A 1500 kg car accelerated at 2 m/s² needs F = 1500 × 2 = 3000 N from the engine (after balancing friction/drag).

Stopping distance

stopping distance = thinking distance + braking distance

• Thinking distance = reaction time × speed (typical reaction time 0.2–0.9 s).
• Braking distance depends on the work done by braking force: ½mv² = F × d → d = mv² / (2F).

Doubling speed quadruples braking distance. This is a classic OCR Higher question.

Factors that increase thinking distance

Tiredness, alcohol, drugs, distractions (phone), age.

Factors that increase braking distance

Wet/icy roads (lower friction), worn tyres, worn brakes, heavier load, higher speed.

Vehicle safety features

Crumple zones, seat belts and airbags all increase the time taken for the occupant to stop.

Using F = Δ(mv) / Δt: a longer Δt means a smaller force on the body, and so reduces injury. They do not change the change in momentum — they spread it over more time.

OCR PAG P10 — investigating force and acceleration

Trolley + light gates: vary force (slotted masses on a string) keeping mass constant; plot a vs F → straight line through origin proves a ∝ F.

OCR exam tip

For a 6-mark "stopping distance" question: structure your answer as thinking + braking, give two examples for each, and include a quantitative point such as "braking distance ∝ v²".