Stopping a vehicle in time
A child steps onto the road 30 m ahead. Change the vehicle's speed, the driver's reaction time and the road, and find the thinking distance, the braking distance and whether it stops in time.
Core concept
Stopping distance = thinking distance (speed × reaction time) + braking distance (v² ÷ 2μg): doubling the speed doubles the first but four-times the second
Topic: Science around us
A driver who sees danger does not brake at once. During the reaction time, about 0.7 s for an alert driver and 1.5 s or more for one looking at a phone, the vehicle keeps going at full speed: How far something travels in a certain time, like kilometres per hour. All key words: that is the thinking distance, v × t. Then the brakes slow it, and friction: A force that slows things down when two surfaces rub together. All key words between tyres and road sets how hard: the braking distance is v² ÷ (2μg), where μ is about 0.7 on a dry road and 0.4 on a wet one. Because the braking distance grows with the square of the speed, going twice as fast needs four times as far to brake. Speeds are in km/h on the road, so we divide by 3.6 to get m/s.
What you will learn
- Find the thinking and braking distances of a vehicle.
- Explain why braking distance grows with the square of the speed.
- Explain how distraction and wet roads make stopping distances longer.
Before you start
- Know distance = speed × time and v² = u² + 2as.
Materials
- A measuring tape and chalk to mark 30 m in the school ground
Equipment
- None
Procedure
- Record 40 km/h, an alert driver (0.7 s), on a dry road.
- Change the speed to 80 km/h and record.
- Back at 40 km/h, change the reaction time to 1.5 s, then the road to wet, recording each.
How this simulation is simplified
- Friction coefficient μ = 0.7 on a dry road and 0.4 on a wet road; g = 9.8 m/s².
- The brakes work fully as soon as the driver presses them.