2.28Forces and braking
Bringing a vehicle to a stop is where the rest of this sub-topic is put to work: reaction times decide how far it travels before the brakes are touched, and forces and energy decide how far it travels afterwards.
The four sections that follow split that into the total stopping distance, the driver's reaction time, the conditions that affect braking, and what braking does to the vehicle.
2.28–2.29Stopping distance
The stopping distance of a vehicle is the sum of the distance the vehicle travels during the driver's reaction time — the thinking distance — and the distance it travels under the braking force, the braking distance. For a given braking force, the greater the speed of the vehicle, the greater the stopping distance.
stopping distance = thinking distance + braking distance
Physics only students should be able to estimate how the distance for a vehicle to make an emergency stop varies over a range of speeds typical for that vehicle, and will be required to interpret graphs relating speed to stopping distance for a range of vehicles.
Worked example
Explain why doubling a car's speed more than doubles its stopping distance.
- Thinking distance is speed × reaction time, so at double the speed the car travels twice as far during the same reaction time — thinking distance doubles.
- Braking distance depends on the kinetic energy that must be removed, and kinetic energy is ½ m v².
- Because the speed is squared, doubling the speed gives four times the kinetic energy.
- For the same braking force, four times the work must be done, so the braking distance is four times as long.
- Adding a doubled thinking distance to a quadrupled braking distance gives a total more than double.
Answer: Thinking distance doubles, but braking distance quadruples because kinetic energy depends on speed squared — so the stopping distance more than doubles.
2.27, 2.30Reaction time
Reaction times vary from person to person. Typical values range from 0.2 s to 0.9 s.
A driver's reaction time can be affected by tiredness, drugs and alcohol. Distractions may also affect a driver's ability to react.
You should be able to explain methods used to measure human reaction times and recall typical results, interpret and evaluate measurements from simple methods to measure the different reaction times of students, and evaluate the effect of various factors on thinking distance based on given data.
The usual method is the ruler drop test. One person holds a ruler vertically between another's open fingers and releases it without warning; the distance the ruler falls before it is caught is converted to a reaction time using a conversion table or the equations of motion.
Repeating it and taking a mean reduces the effect of random variation, and it can be repeated with a distraction — music or conversation — to measure the effect. Points worth making when evaluating the method: the person catching may anticipate the drop if there is any pattern to the timing, and reading the ruler at the top of the fingers rather than the bottom introduces a systematic error.
Common mistake
Tiredness, drugs, alcohol and distractions affect thinking distance, not braking distance. They change how long the driver takes to react, not how well the car stops once the brakes are applied.
2.29, 2.32PFactors affecting braking distance
The braking distance of a vehicle can be affected by adverse road and weather conditions and poor condition of the vehicle.
Adverse road conditions include wet or icy conditions. Poor condition of the vehicle is limited to the vehicle's brakes or tyres — so worn brake pads or bald tyres, and nothing else.
You should be able to explain the factors which affect the distance required for road transport vehicles to come to rest in emergencies, and the implications for safety, and estimate how the distance required for road vehicles to stop in an emergency varies over a range of typical speeds.
The implication for safety is the reason speed limits are lower in towns and why stopping distances are published: a driver cannot shorten their reaction time much, and cannot change the weather, so the one factor under their control is speed — and it is the factor that affects both parts at once.
2.31, 2.33PBraking, energy and large decelerations
When a force is applied to the brakes of a vehicle, work done by the friction force between the brakes and the wheel reduces the kinetic energy of the vehicle, and the temperature of the brakes increases.
That is work done applied to a car: work done against friction raises the temperature, and the energy comes from the kinetic store of the vehicle.
The greater the speed of a vehicle, the greater the braking force needed to stop the vehicle in a certain distance. The greater the braking force, the greater the deceleration of the vehicle. Large decelerations may lead to brakes overheating and/or loss of control.
You should be able to explain the dangers caused by large decelerations. Overheated brakes work less well, so the car may not stop as quickly as the driver expects; and a large braking force can lock the wheels or break the grip between tyres and road, so the driver loses steering control and the vehicle skids.
Higher tier students should be able to estimate the forces involved in the deceleration of road vehicles in typical situations on a public road. The route is F = m a, using an estimated mass for the vehicle and an acceleration worked out from a typical speed and stopping time.
Worked example
Estimate the braking force on a 1500 kg car decelerating from 30 m/s to rest in 4.0 s.
- Find the acceleration: a = ∆v ÷ t = (0 − 30) ÷ 4.0 = −7.5 m/s².
- The negative sign shows it is a deceleration.
- Use F = m a with the magnitude: F = 1500 × 7.5.
- = 11 250 N.
- Round appropriately, since the figures are estimates.
Answer: About 11 000 N, acting in the opposite direction to the motion.
Before you practise
- stopping distance = thinking distance + braking distance.
- Thinking distance depends on speed and on reaction time — tiredness, alcohol, drugs and distractions all lengthen it.
- Braking distance depends on speed, the mass and condition of the vehicle, the brakes and tyres, and the state of the road.
- A typical reaction time is 0.2-0.9 s, and the ruler-drop test measures it.
- Braking distance goes up with the SQUARE of the speed, because the kinetic energy does.
- Braking transfers energy from the kinetic store of the vehicle to the thermal store of the brakes, which get hot.
- A large deceleration means a large braking force, which risks brake overheating and loss of control.