Thinking distance and braking distance, what changes each, reaction times from a ruler drop, and why braking distance goes with speed squared.
What you will learn
- Split a stopping distance into thinking and braking distance
- Measure a reaction time with a ruler drop
- Explain why doubling the speed makes the braking distance four times as long
Two distances, added
When a driver sees a hazard, the car keeps going while the driver reacts, then slows down once the brakes are on.
stopping distance = thinking distance + braking distance
thinking distance = speed × reaction time
Typical reaction times are 0.2 s to 0.9 s. Tiredness, alcohol, drugs and phones make them longer, so they change the thinking distance. Wet or icy roads and worn tyres or brakes change the braking distance: there is less friction between the tyres and the road.
Thinking distance is directly proportional to speed (double the speed, double the thinking distance). Rearranged: reaction time = thinking distance ÷ speed. The braking distance comes from v² − u² = 2as: from speed u to a stop, braking distance = u² ÷ 2a.
Speed changes both. That is why the speed limit near a school matters so much.
The rest of this lesson and its 11 practice questions are locked.
In this lesson
- Two distances, added
- Measuring a reaction time
- Why speed squared
- Try it: Braking force and acceleration
11 practice questions, marked as you go; about 20 minutes in all.
Key terms
Thinking, Braking
In this unit: Forces and motion
Speed, velocity and acceleration, the graphs that show them, the equations of motion, Newton's laws and stopping distances.