# 5.8.5 Factors Affecting Braking Distance

### Factors Affecting Braking Distance

• The braking distance is the distance travelled by a car under the braking force – i.e. whilst it is slowing down
• The main factor affecting the braking distance of a car is its speed
• There are additional factors which affect the braking distance, such as:
• Vehicle condition – e.g. worn tyres or poor brakes
• Road condition – wet or icy roads make it harder to decelerate
• Vehicle mass – a heavy vehicle, such as a lorry, takes longer to stop

### Braking & Friction

• When a driver applies the brakes, there is a frictional force between the brakes and the wheels of the car
• This frictional force does work on the brakes – i.e. it transfers energy from the car to the brakes
• Therefore, the kinetic energy of the car decreases and the thermal energy of the brakes increases – i.e. the brakes heat up
• This means the car decelerates (slows down) Work done by breaking transfers kinetic into thermal energy

### Braking Force & Speed

• The greater the speed of a vehicle, the greater the braking force required to bring the vehicle to a halt for a given distance
• Since the braking force would need to be larger, the deceleration of the vehicle will be large as well
• This is due to the link between resultant force and acceleration as stated in Newton's second law of motion
• Large decelerations could lead to the brakes overheating and / or loss of control of the vehicle

#### Worked Example

A car is travelling at 15 m/s when the driver applies the brakes. The car decelerates uniformly and stops.

The mass of the car and the driver is 1500 kg, and together they have a total kinetic energy of 168 750 J.

(a) How much work is done by the braking force to stop the car and the driver?

(b) The braking force used to stop the car and the driver was 6000 N. Calculate the braking distance of the car.

Part (a)

Step 1: Recall the process of applying brakes to a vehicle

• The work done is the energy transferred from the car and driver to the brakes
• This energy transfer is from kinetic energy to thermal energy
• In this case, the car is brought to a complete stop, so 168 750 J of energy is transferred from kinetic energy to heating up the brakes (assuming all energy is transferred to heat only!)

Part (b)

Step 1: State the equation for work done

Work done = Force × distance travelled (or W = Fs)

• In this case, the force doing the work (transferring energy) is the braking force

Step 2: Rearrange the equation and solve for distance travelled

Distance travelled = Work done ÷ Force

Step 3: Substitute the values for work and force

Distance = 168 750 ÷ 6000 = 28.1 m

• Hence the braking distance (the distance travelled by the car under the braking force) is 28.1 m

#### Exam Tip

If you are asked to explain why the temperature of the brakes increases when a vehicle stops, remember, work is done by the frictional force between the brakes and the wheel.

It’s a common mistake to write about the friction between the wheels and the road. This does happen, but in this case, the wheels heat up the road! The brake temperature increases because there is a transfer of energy from the car’s kinetic energy to the thermal energy of the brakes. ### Author: Jonathan

Jonathan graduated with a first-class Master's degree in Theoretical Physics from Imperial College London. He has worked in education for more than a decade as a Maths and Physics Teacher, Tutor, Head of Physics, and most recently, as Assistant Headteacher. He is now an Educational Consultant and works with us to design and improve our Physics resources.
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