## Forces & Braking

The stopping distance of a vehicle is the sum of the distance the vehicle travels during the driver’s reaction time (thinking distance) and the distance it travels under the braking force (braking distance). For a given braking force the greater the speed of the vehicle, the greater the stopping distance.

total stopping distance = thinking distance + braking distance

## Thinking Distance

The thinking distance is the distance a car travels while the driver reacts to needing to brake

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Reaction times vary from person to person. Typical values range from 0.2 s to 0.9 s.

A driver’s reaction time can be affected by tiredness, drugs and alcohol. Distractions may also affect a driver’s ability to react.

## Braking Distance

The braking distance is the distance the car travels whilst the brakes are applied

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The braking distance of a vehicle can be affected by adverse road and weather conditions and poor condition of the vehicle.

Adverse road conditions include wet or icy conditions. Poor condition of the vehicle is limited to the vehicle’s brakes or tyres.

A force is applied to the brakes of a vehicle, work done by the friction force between the brakes and the wheel reduces the kinetic energy of the vehicle and the temperature of the brakes increases.

The greater the speed of a vehicle the greater the braking force needed to stop the vehicle in a certain distance.

The greater the braking force the greater the deceleration of the vehicle. Large decelerations may lead to brakes overheating and/or loss of control.

You can estimate the forces involved in the deceleration of road vehicles in typical situations on a public road.

Step 1: Calculate the Acceleration of the car as it stops

final velocity² – initial velocity² = 2 × acceleration × distance

02 – 13.42 = 2 x acceleration x 23

179.56 = 46 x acceleration

acceleration = 179.56 / 46

acceleration = 3.9 m/s2

Step 2: Calculate the Force needed to stop

force = mass x acceleration

force = 1150 x 3.9

The force needed to stop the car is 4485 Newtons

## Momentum (unit: kgm/s)

Momentum is a quantity that every moving object has. Momentum is a vector quantity. A stationary object has zero momentum.

Momentum is defined by the equation:

momentum = mass × velocity

momentum = mass × velocity

200 = mass x 3.2

mass = 200 / 3.2

The mass of the skater is 62.5 kg

In a closed system, the total momentum before an event is equal to the total momentum after the event. This is called conservation of momentum.

total momentum before event = total momentum after event

The conservation of momentum can be used to solve problems about collisions and explosions.

• (total) momentum before (collision) = (total) momentum after (collision)
• momentum of skater A decreases and momentum of skater B increases
• velocity of skater A decreases and velocity of Skater B increases

total momentum before event = total momentum after event

momentum before event = (mass of skateboarder x velocity of skate boarder) + (mass of skateboard x velocity of skate board)

momentum before event = (42 x 0) + (1.8 x 0) = 0 kgs/s

Momentum before event = Momentum after event = (momentum of skater + momentum of skateboard)

0 = (mass of skateboarder x velocity of skate boarder) + (mass of skateboard x velocity of skate board)

0 = (42 x 0.3) + (1.8 x velocity of skateboard)

-12.6 = 1.8 x velocity of skate board

velocity of skate board = -12.6 / 1.8

velocity of skateboard = -7 m/s

The velocity of the skate board is 7m/s in the opposite direction to the skateboarder

## Changes in Momentum (Triple Physics Only)

When a force acts on an object that is moving, or able to move, a change in momentum occurs.

Force equals the rate of change of momentum.

force = change in momentum/time taken

force = change in momentum/time taken

12 = change in momentum / 60

change in momentum = 12 x 60

The change in momentum is 720 kgm/s

Many safety features use this concept to keep us safe, for example: air bags, seat belts, gymnasium crash mats, cycle helmets and cushioned surfaces for playgrounds.

The safety features all:

• increase the time taken for the change of momentum to happen
• which decreases the rate of change of momentum
• which reduces the force acting
• the seat belt stretches
• so driver takes a longer time to slow down and stop (than a driver hitting a hard surface / windscreen / steering wheel)
• for the (same) change of momentum
• a smaller force is exerted (so driver less likely to have serious injury than driver without seat belt)