Forces and motion, Year 11: stopping distance and braking

thinking; braking

HintFirst the driver has to react; then the car has to slow down.

The whyThe first part is how far the vehicle goes while the driver is still reacting, before the brakes are even pressed. The second is how far it travels while the braking force brings it to rest. Adding the two gives the total distance needed to stop.

Thinking distance

HintIt is covered before the driver's foot has even reached the pedal.

The whyDuring the reaction time the vehicle carries on at its original speed, so this distance is speed × reaction time. Anything that slows the driver's reactions makes it longer; the state of the road and the brakes makes no difference to it.

Both

HintConsider how far the car goes while the driver reacts, and then how much energy the brakes must remove.

The whyAt a higher speed the car covers more ground during the same reaction time, so the thinking distance grows. It also has more kinetic energy for the brakes to remove, so for the same braking force the braking distance grows as well. The greater the speed, the greater the stopping distance.

0.2; 0.9

HintBoth are less than one second.

The whyReaction time is the delay between seeing a hazard and starting to act. It varies from person to person and from moment to moment, and these are the typical limits AQA expects pupils to recall. Measuring it is covered in Biology, where it is a required practical.

tiredness; alcohol; distractions

HintThink about the state of the driver, and about what else might hold their attention.

The whyTiredness, alcohol and some drugs, including some medicines, slow the nervous system, and a distraction such as a phone takes the driver's attention away from the road. A longer reaction time means a longer thinking distance, and so a longer stopping distance.

21

HintThe car keeps its full speed for the whole of the reaction time.

The whyThinking distance = speed × reaction time, which is just distance = speed × time for the moments before the brakes go on. Here that is 30 × 0.7. At motorway speed a car travels the length of about five cars before the driver has even touched the pedal.

The thinking distance doubles; the braking distance does not change

HintOnly one of the two has anything to do with the driver's nervous system.

The whyThinking distance is speed × reaction time, so doubling the reaction time at a fixed speed doubles it. Braking distance depends on the speed, the brakes, the tyres and the road, none of which has changed. The stopping distance still rises, because it is the sum of the two.

0.9 s

HintRearrange distance = speed × time for the longer of the two distances.

The whyReaction time = thinking distance ÷ speed = 18 ÷ 20. Alert, the same driver's reaction time is 12 ÷ 20 = 0.6 s, so the distraction has added 0.3 s and six metres. Working back from given data like this is how AQA expects the effect of a factor to be evaluated.

wet; icy

HintThink of what rain and a hard frost each leave on the tarmac.

The whyWater or ice between the tyre and the road reduces the friction that can act, so the largest possible braking force is smaller. With a smaller force slowing it, the vehicle travels further before it stops. These are the two adverse road conditions AQA names.

The brakes and the tyres

HintOne pair of parts grips the wheels; the other grips the road.

The whyWorn brakes cannot press on the wheels as hard, and tyres with little tread cannot grip the road as well, especially in the wet. Either way the braking force is smaller, so the vehicle needs more distance to stop. AQA limits 'poor condition of the vehicle' to these two.

There is less friction between the tyres and the road

HintThink about how well rubber grips a surface with a film of water on it.

The whyBraking relies on the road pushing backwards on the tyres. Water acts as a lubricant, so the tyres slide more easily and the force slowing the car is smaller. A smaller force gives a smaller deceleration, so the car covers more distance before it comes to rest.

About 56 m (four times as far)

HintThe brakes must remove the car's kinetic energy, which depends on speed squared.

The whyDoubling the speed gives the car four times the kinetic energy. The brakes remove energy by doing work, and work = force × distance, so with the same force they need four times the distance: 4 × 14 m. The Highway Code's typical figures are 14 m at 30 mph and 55 m at 60 mph.

The braking distance only

HintAsk whether rain changes the driver or the grip.

The whyThinking distance depends on the speed and the driver's reaction time, and neither has changed. Braking distance depends on the friction available between tyres and road, which a wet surface reduces. This is why drivers are advised to leave a much bigger gap in the wet.

work

HintIt is the quantity calculated as force × distance.

The whyA force acting through a distance transfers energy. Here the friction force acts while the wheel turns against the brake, and the energy leaves the car's kinetic store and raises the temperature of the brakes. The car stops when all of its kinetic energy has been transferred.

overheat; control

HintOne danger concerns where the car's energy ends up; the other concerns the tyres' grip.

The whyA large deceleration needs a large braking force, and a great deal of energy is transferred to the brakes in a short time, so their temperature rises sharply. The tyres may also lose their grip on the road, so that the car skids and cannot be steered.

It has more kinetic energy, so more work must be done in the same distance

HintThink about what the brakes have to remove from each car.

The whyThe brakes have to transfer all of the car's kinetic energy. Work done = force × distance, so if the distance is fixed and the energy to remove is bigger, the force must be bigger. So a faster vehicle needs a bigger force from its brakes if it is to stop in the same space.

deceleration

HintNewton's second law links a force to how quickly the velocity changes.

The whyFrom F = m a, a bigger resultant force on the same mass gives a bigger rate of change of velocity. When that force acts against the motion, the vehicle slows more sharply and stops in a shorter time and distance.

About 9000 N

HintEstimate the deceleration first, then use Newton's second law.

The whyDeceleration ~ change in velocity ÷ time = 30 ÷ 5 = 6 m/s². Then F = m a ~ 1500 × 6 newtons. The figures are rough, so the answer is an estimate: braking forces on a car in an emergency stop are of the order of thousands of newtons.