# 5.8.6 Estimating Decelerating Forces

Higher Tier Only

### Estimating Decelerating Forces

• The work done by the brakes when a vehicle slows to a halt is given by the following equation: This equation shows the work done (energy transferred) by the brakes on the wheels of a car

• This equation shows that:
• The work done is the transfer of kinetic energy
• The braking distance is proportional to the speed squared (if the speed is doubled, the distance increases 4 times)
• We can use this equation to estimate the decelerating forces required for a typical vehicle moving at everyday speeds

#### Worked Example

At 18 m/s (40 mph) the braking distance of a typical car of mass 1500 kg is about 24 m.

Use this information to estimate the braking force for a typical car. #### Exam Tip

You should be able to deduce from the equation that the braking distance is proportional to the vehicle’s speed2. Note, this actually doesn’t apply at very high speeds because the brakes get hot and become less effective. This reduces the braking force, causing the braking distance to increase even further. ### Author: Jonathan

Jonathan graduated with a first-class Master's degree in Theoretical Physics from Imperial College London. He has worked in education for more than a decade as a Maths and Physics Teacher, Tutor, Head of Physics, and most recently, as Assistant Headteacher. He is now an Educational Consultant and works with us to design and improve our Physics resources.
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