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

To estimate the kinetic energy (KE) of the car, we use the formula:

$KE = \frac{1}{2}mv^2$

Where:

• $m$ is the mass of the car (we'll assume an average mass of about 1000 kg for a typical car).
• $v$ is the velocity in meters per second.

First, we convert the speed from km/h to m/s:

$v = 100 \text{ km/h} = \frac{100 \times 1000}{3600} \approx 27.78 \text{ m/s}$

Next, substituting the values into the kinetic energy formula:

$KE = \frac{1}{2} \times 1000 \text{ kg} \times (27.78 \text{ m/s})^2$

Calculating this gives:

$KE \approx 0.5 \times 1000 \times 771.84 \approx 385920 \text{ J}$

This approximation yields $3.86 \times 10^5 \text{ J}$, which suggests that the answer is closest to $10^6 \text{ J}$ (one million joules).