Stopping distance depends on driver, vehicle and road

1. Thinking distance depends on the vehicle's speed and the driver's reaction time.
2. Braking distance depends on speed, vehicle mass, brake condition, road condition and the friction between the tyres and road.
3. Any factor that increases either part increases the total stopping distance.

Speed increases both parts

1. At a fixed reaction time, thinking distance increases in direct proportion to speed because $d=vt$.
2. The kinetic energy store is $E_k=\frac{1}{2}m{v}^2$, so doubling speed gives four times the kinetic energy.
3. The brakes must transfer this extra energy, so braking distance rises much more sharply than thinking distance if braking force is similar.

Mass and braking force affect deceleration

1. A greater mass gives a greater kinetic energy store at the same speed because $E_k=\frac{1}{2}m{v}^2$.
2. For the same braking force, a greater mass also produces a smaller deceleration because $a=\frac{F}{m}$.
3. Both links mean that a more massive vehicle needs a longer braking distance under the same conditions.
4. Worn or overheated brakes can produce a smaller braking force, giving a smaller deceleration and a longer braking distance.

Road and tyres control friction

1. Water, ice, loose gravel or mud can reduce tyre-road friction, reducing the maximum braking force.
2. Worn tyres, low tread depth or unsuitable tyre pressure can reduce grip and increase braking distance.
3. A smaller braking force produces a smaller deceleration, so the vehicle travels farther before stopping.
4. Anti-lock braking systems help prevent the wheels locking, allowing the tyres to keep grip and the driver to retain steering control.

Driver factors change reaction time

1. Alcohol, illegal drugs and some medicines can slow nervous-system processing and muscle response.
2. Mobile phones, passengers, eating, loud music and adjusting controls divert attention from the road.
3. Tiredness reduces alertness and can delay hazard detection and response.
4. A longer reaction time increases thinking distance because the vehicle continues at its original speed for longer before braking.

Calculations connect energy and distance

1. If the mean braking force is treated as constant, the work done by the brakes is $W=Fs$.
2. Equating work done with the initial kinetic energy gives $Fs=\frac{1}{2}m{v}^2$, so $s=\frac{m{v}^2}{2F}$.
3. This model shows why braking distance increases with mass and with the square of speed, but decreases when braking force increases.

Every factor acts through distance or force

1. Driver factors alter reaction time and therefore thinking distance.
2. Vehicle and road factors alter kinetic energy, braking force or deceleration and therefore braking distance.