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 a car, we use the formula:

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

where:

• m is the mass of the car (in kg)
• v is the speed of the car (in m/s)

1. Convert speed from km/h to m/s:

   • Since 1 km = 1000 m and 1 hour = 3600 seconds: $v = 100 \text{ km/h} = \frac{1000 \, \text{m}}{3600 \, \text{s}} \approx 27.78 \, \text{m/s}$

2. Assuming a typical mass of a car (m) is about 1000 kg:

   • Now substitute the values into the kinetic energy formula: $KE = \frac{1}{2} \times 1000 \, \text{kg} \times (27.78 \, \text{m/s})^2$

3. Calculate:

   • $KE \approx \frac{1}{2} \times 1000 \times 771.38 \approx 385690 \, \text{J}$
   • Which can be approximated as 3.85 x 10⁵ J, and rounded down estimates lead us to select:
   • Therefore, the answer is B: 10⁵ J.