Study Notes
Overview
Stopping distance is a classic physics topic that combines concepts of motion, forces, and energy. For an examiner, it is a perfect way to test a candidate's ability to distinguish between different physical concepts and apply them to a real-world safety scenario. This guide will deconstruct the topic into two key parts: the driver's reaction time (thinking distance) and the vehicle's braking mechanics (braking distance). You will learn the factors that influence each, the mathematical models used to describe them, and how they combine to determine the total stopping distance. Expect to see this topic appear in your exam as both short-answer definition questions and longer, 6-mark extended-response questions, particularly on the Higher Tier paper where calculations involving kinetic energy are common.
Key Concepts
Concept 1: Thinking Distance
Thinking distance is the distance the vehicle travels during the driver's reaction time. This is the time interval between the driver spotting a hazard and physically applying the brakes. During this period, the car continues to travel at a constant velocity. The key relationship is straightforward: Thinking Distance = Speed × Reaction Time. This means thinking distance is directly proportional to the vehicle's speed. If you double your speed, you will double your thinking distance, assuming your reaction time remains constant. A typical reaction time for a focused driver is around 0.7 seconds, but this can be significantly longer.
Example: A car is travelling at 20 m/s. The driver has a reaction time of 0.8 seconds. The thinking distance would be 20 m/s × 0.8 s = 16 metres.
Concept 2: Braking Distance
Braking distance is the distance the vehicle travels from the moment the brakes are applied until it comes to a complete stop. This is governed by the principles of work and energy. To stop the car, the brakes must do work to dissipate the car's kinetic energy as heat. The work done by the braking force is equal to the initial kinetic energy of the vehicle. This gives us the crucial equation for Higher Tier candidates: Work Done by Brakes = Kinetic Energy of Vehicle, or F × d = ½ × m × v², where F is the braking force, d is the braking distance, m is the mass, and v is the velocity.
From this, we can see that braking distance (d) is proportional to the square of the velocity (v²). This is a vital relationship to remember. If you double your speed, you quadruple your braking distance (2² = 4). If you triple your speed, your braking distance increases by a factor of nine (3² = 9).
Mathematical/Scientific Relationships
Here are the key formulas you need to know for the Stopping Distance topic.
- Stopping Distance = Thinking Distance + Braking Distance (Must memorise)
- Thinking Distance = Speed × Reaction Time (Must memorise)
- Kinetic Energy (KE) = ½mv² (Given on formula sheet)
- Work Done = Force × Distance (Given on formula sheet)
- Fd = ½mv² (Higher Tier - derived, but must understand and apply)
Symbol Meanings:
- d: distance (in metres, m)
- v: speed or velocity (in metres per second, m/s)
- t: time (in seconds, s)
- m: mass (in kilograms, kg)
- F: force (in Newtons, N)
- KE: Kinetic Energy (in Joules, J)
Practical Applications
Understanding stopping distance is fundamental to road safety design and regulations. It informs speed limits, the design of braking systems (like ABS), and public safety campaigns about the dangers of drink-driving or using a phone at the wheel. The concepts are also applied in accident investigation to determine vehicle speeds prior to a collision. There isn't a specific required practical on stopping distance, but questions often use data from experiments measuring reaction times (e.g., the ruler drop test) or investigating friction.
