a) A motorcyclist is climbing a hill at a constant speed of 13 m/s - Edexcel - GCSE Physics - Question 3 - 2017 - Paper 1

In the railway system described, the design utilizes gravitational potential energy effectively. When one passenger cabin descends, the gravitational potential energy of that cabin decreases, which in turn is converted into kinetic energy as it moves downwards. This kinetic energy is then transferred to the opposite cabin, which is lifted upwards. Thus, the system maintains a balance, as the energy lost by one cabin is gained by the other, showcasing efficient energy transfer and minimizing energy wastage.

The value of the kinetic energy (KE) of the car when the brakes were applied equals the work done to stop it, which is 510 000 J.

To calculate the velocity, we can use the formula for kinetic energy:

where:

• $KE$ is the kinetic energy (510 000 J)
• $m$ is the mass (1400 kg)

Rearranging the formula gives:

Substituting the values:

Calculating this gives approximately:

Using the work-energy principle, the work done by the brakes to stop the car can be calculated using:

where:

• $W$ is the work done (510 000 J)
• $F$ is the average force (15 000 N)
• $d$ is the distance

Rearranging gives:

Substituting the values:

Thus, the distance it takes for the brakes to stop the car is 34 meters.