Estimating Decelerating Forces (OCR GCSE Physics A (Gateway)): Revision Note

At 18 m s^-1 (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. 

Answer:

Step 1: List the known quantities

• Mass, m=1500 kg

• Braking distance, s=24 m

• Speed, v=18 m/s

Step 2: State the relevant equation

$\mathrm{Braking}\mathrm{force}\times \mathrm{braking}\mathrm{distance}=\frac{1}{2}{\mathrm{mv}}^2$

Step 3: Rearrange for the braking force

$\mathrm{Braking}\mathrm{force}=\frac{{\displaystyle \frac{1}{2}}{\mathrm{mv}}^2}{\mathrm{braking}\mathrm{distance}}$

Step 4: Substitute the values into the equation

$\mathrm{Braking}\mathrm{force}=\frac{{\displaystyle \frac{1}{2}}\times 1500\times {\left(18\right)}^2}{24}=10125\mathrm{N}$

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.