Factors affecting braking distance 1

This transfer explains why brakes get hot and their temperature increases. The work done to stop the vehicle is exactly equal to its initial kinetic energy:

$$Fd = \frac{1}{2}mv^2$$

If a very large braking force is applied to stop quickly, the deceleration is huge. This can cause the brakes to overheat or the wheels to lock, leading the car to skid and the driver to lose control.

Worked Example: Calculating Braking Force

A 1500 kg car traveling at 20 m/s stops in 40 m. Calculate the braking force required.

Step 1: Calculate the initial kinetic energy.

• $E_k = \frac{1}{2}mv^2$
• $E_k = 0.5 \times 1500 \times 20^2 = 300,000$ J

Step 2: Equate work done to kinetic energy.

• Work done = Kinetic energy
• $F \times d = 300,000$ J
• $F \times 40 = 300,000$

Step 3: Rearrange and solve for force ($F$).

• $F = 300,000 / 40$
• $F = 7,500$ N

How Conditions Affect Braking Distance

Examiners often ask you to explain exactly why poor conditions increase braking distance. The causal chain always comes back to friction and energy. Adverse road conditions, such as wet or icy roads, result in reduced friction between the vehicle's tyres and the road surface. In wet conditions, the braking distance is approximately doubled, while on icy roads it can be up to 10 times greater.

The condition of the vehicle also matters heavily. Worn tyres with low tread depth (below the legal limit of 1.6 mm) cannot effectively disperse water. This causes a layer of water to build up between the tyre and the road, a dangerous effect known as aquaplaning, which severely reduces friction. Similarly, worn brakes provide a smaller braking force for the same pedal pressure.

If friction or braking force is reduced, less work is done per metre of travel. Therefore, a much longer distance is required for the work done by the brakes to dissipate the vehicle's kinetic energy. Increasing the mass of the car also increases its kinetic energy ($E_k = \frac{1}{2}mv^2$), meaning a greater distance is needed to do the extra work to stop it.

Estimating Braking Distance from Speed

It is a common misconception that doubling your speed simply doubles your braking distance. In reality, braking distance is directly proportional to the square of the speed ($d \propto v^2$).

This non-linear relationship means:

• If speed doubles ($\times 2$), the braking distance increases by a factor of four ($2^2 = 4$).
• If speed triples ($\times 3$), the braking distance increases by nine times ($3^2 = 9$).

To estimate braking distances in an exam, you can use known values and apply this $v^2$ rule. For example, the Highway Code states that at 20 mph, the typical braking distance in dry conditions is 6 m. At 40 mph (double the speed), the braking distance becomes $6 \times 4 = 24$ m.

Worked Example: Estimating Braking Distance

A car traveling at 10 m/s has a braking distance of 10 m. Estimate the braking distance at 30 m/s.

Step 1: Identify the factor by which the speed has changed.

• Speed change factor = $30 / 10 = 3$

Step 2: Apply the $v^2$ proportionality rule.

• Distance increases by the square of the speed factor.
• Multiplier = $3^2 = 9$

Step 3: Calculate the new estimated braking distance.

• New distance = $10$ m $\times 9 = 90$ m