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

The design of the railway system allows for effective energy transfer between the two passenger cabins. When one cabin descends, it utilizes gravitational potential energy, which is then transferred to the other cabin that ascends, converting that potential energy into kinetic energy. This means that the energy lost by the descending cabin aids the ascent of the opposite cabin, thereby conserving energy within the system and minimizing the need for additional power inputs.

The work done to stop the car, which is 510,000 J, is equal to the kinetic energy of the car when the brakes were first applied. Therefore, the kinetic energy is 510,000 J.

To find the velocity of the car, we can use the kinetic energy formula:

Here, we already know:

• $KE = 510,000 \, \text{J}$
• $m = 1400 \, \text{kg}$

Rearranging the formula to solve for $v$ gives us:

v = \sqrt{\frac{2 \times 510,000}{1400}} \approx 27 , \text{m/s}

To calculate the stopping distance, we can use the work-energy principle:

The work done to stop the car is equal to the force applied multiplied by the distance. Given that the average force from the brakes is 15,000 N, we rearrange the formula to solve for distance:

Hence, the distance it takes for the brakes to stop the car is 34 m.