During a different part of the journey the car accelerates from 9 m/s to 18 m/s in 6 s - AQA - GCSE Physics - Question 10 - 2018 - Paper 1

The correct equation that links acceleration, mass, and resultant force is:

resultant force = mass x acceleration.

To calculate the resultant force, we first need to find the total mass:

• Total mass = Mass of the car + Mass of the driver = 1120 kg + 80 kg = 1200 kg.

Using the formula:

$$F = m \times a,$$

where the mass (m) is 1200 kg and the acceleration (a) is 1.5 m/s²:

$$F = 1200 \text{ kg} \times 1.5 \text{ m/s}^2 = 1800 \text{ N}.$$

Therefore, the resultant force is 1800 N.

When the speed of the car doubles, the kinetic energy increases by a factor of 4.

This is because kinetic energy (KE) is given by the formula:

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

where m is mass and v is velocity.

If the speed doubles, the new kinetic energy becomes:

$$KE_{new} = \frac{1}{2} m (2v)^2 = 2mv^2 = 4 \times KE_{original}.$$

Since the braking force remains constant, the increased kinetic energy requires a longer stopping distance. Therefore, if the speed doubles, the braking distance also increases by a factor of 4.