Newton's laws and stopping distances

Physics · Forces. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Newton's first law: if the resultant force on an object is zero, it stays at rest or keeps moving at a steady velocity. A car at steady speed on a level road has a driving force equal to the resistive forces. The tendency to stay at rest or in uniform motion is called inertia.

Second law: a resultant force causes an acceleration. The acceleration is proportional to the force and inversely proportional to the mass. Third law: when two objects interact, they exert equal and opposite forces on each other.

The stopping distance of a vehicle has two parts: the distance travelled during the driver's reaction time, and the distance travelled while the brakes act.

Rules to remember

Common mistake

Students use the applied force in F = ma instead of the resultant force. Subtract friction and other opposing forces first.

Worked example

A car of mass 1500 kg travels at 30 m/s. The driver's reaction time is 0.60 s and the braking force is 7500 N. What is the stopping distance?

  1. Thinking distance = speed × reaction time = 30 × 0.60 = 18 m.
  2. Deceleration = F ÷ m = 7500 ÷ 1500 = 5.0 m/s2.
  3. Braking distance from v2 − u2 = 2as: s = 302 ÷ (2 × 5.0) = 900 ÷ 10 = 90 m.
  4. Stopping distance = 18 + 90 = 108 m.

Answer: 108 m

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