A car travels at 100 km h⁻¹ on a motorway - AQA - A-Level Physics - Question 9 - 2022 - Paper 1

The formula for kinetic energy (KE) is given by: $KE = \frac{1}{2} mv^2$ where m is mass and v is velocity.

To estimate the kinetic energy, we need to determine a suitable mass for the car. For a typical car, the mass can be approximately 1000 kg.

Next, we convert the velocity to meters per second (m/s): $100\, \text{km h}^{-1} = \frac{100\, \text{km}}{1\, \text{h}} \times \frac{1000\, \text{m}}{1\, \text{km}} \times \frac{1\, \text{h}}{3600\, \text{s}} = \frac{100000}{3600} \approx 27.78\, \text{m s}^{-1}$

Now we can substitute these values into the kinetic energy formula: $KE = \frac{1}{2} \times 1000\, \text{kg} \times (27.78\, \text{m s}^{-1})^2$ Calculating this gives: $KE \approx \frac{1}{2} \times 1000 \times 771.84 \approx 385920\, \text{J}$

Thus, the estimated kinetic energy is approximately $3.86 \times 10^5 \, \text{J}$.