Stopping Distances, Braking and Momentum
What Are Stopping Distances?
When a vehicle needs to stop, it doesn't happen instantly. The stopping distance is made up of two parts: thinking distance and braking distance.
Stopping distance = thinking distance + braking distance
The thinking distance is how far the car travels while the driver reacts to a hazard. During this time, the vehicle continues at constant speed.
The braking distance is how far the car travels while the brakes are being applied and the vehicle is decelerating.
Several factors can increase thinking distance:
- Tiredness or fatigue reduces reaction speed
- Drugs and alcohol slow down the nervous system
- Distractions like mobile phones delay reactions
- Higher speeds mean more distance covered during reaction time
Braking Forces and Energy
When brakes are applied, friction between the brake pads and wheels creates a force that opposes motion. This braking force does work against the vehicle's kinetic energy.
The work done by braking forces transfers the vehicle's kinetic energy into heat energy at the brakes. We can calculate this using:
$$\text{Work done by brakes} = \text{Braking force} \times \text{Braking distance}$$
This work done equals the kinetic energy that was lost: \(\frac{1}{2}mv^2\)
Braking distance is proportional to the square of speed. Double the speed means four times the braking distance.
Braking distance increases when:
- Vehicle speed is higher — kinetic energy increases with speed squared
- Vehicle mass is greater — more kinetic energy to remove
- Road conditions are poor — wet or icy roads reduce friction
- Brake or tyre condition is poor — worn components reduce braking force
Understanding Momentum
Every moving object has momentum. Momentum is calculated using:
$$\text{momentum} = \text{mass} \times \text{velocity}$$
$$p = m \times v$$
Momentum is measured in kg⋅m/s and is a vector quantity — it has both size and direction.
In any collision or explosion, the total momentum before equals the total momentum after. This is the conservation of momentum.
For two objects colliding:
$$m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$$
Where \(u\) represents initial velocities and \(v\) represents final velocities.
Separate Physics only. Force as the rate of change of momentum, and the safety features that depend on it, are not examined on Combined Science. Read this section for interest.
Vehicle Safety Features
Modern vehicles use momentum principles to improve safety during collisions. The key is to increase the time over which momentum changes occur.
Using \(F = \frac{\Delta p}{\Delta t}\), we can see that increasing the time (\(\Delta t\)) for a momentum change reduces the force experienced.
Safety features work by increasing collision time, which reduces the forces acting on passengers.
Examples of safety features include:
- Crumple zones — designed to deform and extend collision time
- Airbags — inflate to cushion impact and increase stopping time
- Seat belts — stretch slightly to reduce peak forces on the body
- ABS brakes — prevent wheel locking to maintain steering control