Physics on the Move: Stopping Distances and Momentum
Stopping Distance
When a driver sees a hazard and brings a vehicle to rest, the vehicle travels a total distance called the stopping distance. This splits into two parts:
Thinking distance is the distance the vehicle travels during the driver’s reaction time — between seeing the hazard and pressing the brake. Typical human reaction time is roughly 0.2–0.9 seconds. Anything that slows the driver’s reaction increases thinking distance: tiredness, alcohol, drugs and distractions such as mobile phone use all have this effect. Thinking distance is directly proportional to speed — double the speed, double the thinking distance.
Braking distance is the distance travelled after the brakes are applied until the car stops. During braking, kinetic energy is transferred to heat energy in the brakes by friction. Factors that increase braking distance include: higher speed (much more kinetic energy to dissipate), wet or icy roads (less friction between tyres and road), worn tyres (less grip), and worn or poorly maintained brakes (less braking force).
Stopping distance = thinking distance + braking distance. Thinking distance is affected by the driver (reaction time). Braking distance is affected by the vehicle and road conditions. At higher speeds, both distances increase — but braking distance increases much more because kinetic energy is proportional to speed squared.
A common error is to assume that alcohol or tiredness affects braking distance. They do not — they slow the driver’s reaction, which increases thinking distance only. Road conditions (wet, icy) and vehicle condition (tyre wear, brake wear) affect braking distance only. Speed affects both.
Momentum
Momentum is a property of all moving objects. It depends on both mass and velocity:
$$p = m \times v$$
where \(p\) = momentum in kg m/s, \(m\) = mass in kg, and \(v\) = velocity in m/s. Momentum is a vector quantity — it has both magnitude and direction. A lorry moving at 15 m/s has far greater momentum than a bicycle moving at the same speed, simply because of its much larger mass.
A car has a mass of 1200 kg and is travelling at 20 m/s. Calculate its momentum.
Step 1: Write the equation. \(p = m \times v\)
Step 2: Substitute. \(p = 1200 \times 20 = 24{,}000 \text{ kg m/s}\)
Step 3: State units. The momentum of the car is 24,000 kg m/s in the direction of travel. If the car brakes to rest, all of this momentum must be transferred (to the brake pads as heat, and to the road via tyre friction).
Conservation of Momentum
The law of conservation of momentum states that the total momentum of a closed system (no external forces) does not change. In any collision or explosion:
$$\text{total momentum before} = \text{total momentum after}$$
This is one of the most powerful laws in physics because it applies to every collision — from subatomic particles to spacecraft docking. If two objects collide and stick together, the combined mass moves at a lower velocity so that momentum is conserved.
A 1000 kg car moving at 12 m/s collides with and sticks to a stationary 500 kg car. What is the velocity of the combined vehicles after the collision?
Step 1: Calculate total momentum before. Car 1: \(p = 1000 \times 12 = 12{,}000\) kg m/s. Car 2 is stationary: \(p = 500 \times 0 = 0\) kg m/s. Total before = 12,000 kg m/s.
Step 2: Apply conservation. Total momentum after = 12,000 kg m/s. Combined mass = 1000 + 500 = 1500 kg.
Step 3: Find velocity. \(v = \frac{p}{m} = \frac{12{,}000}{1500} = 8 \text{ m/s}\) in the original direction of travel.
Conservation of momentum: total momentum before a collision equals total momentum after (in a closed system). \(p = mv\) gives momentum in kg m/s. Momentum is a vector — direction matters.
Safety Features and Large Decelerations
Rapid deceleration is dangerous because the force on the body is large. From Newton’s Second Law, \(F = ma\); large negative acceleration (rapid stopping) means large force on vehicle occupants. Modern vehicles use several design features to reduce injury by extending the time over which momentum changes:
Crumple zones at the front and rear of cars deform gradually in a crash, increasing the time for momentum to change and so reducing the peak force on occupants. Seatbelts stretch slightly, extending the stopping time for the passenger and reducing the peak force compared with hitting a rigid surface. Airbags inflate rapidly and deflate as the occupant hits them, spreading the impact force over a larger area and a longer time.
The same change in momentum spread over a longer time gives a smaller force. This is why crumple zones, seatbelts and airbags all work: they make the collision last longer, so the force on the people inside is smaller. You explain this in words — this spec gives you no equation for it.