Given: Initial velocity u = 0 m/s, acceleration a = 5 m/s2, final velocity v = 25 m/s.

Given: Initial velocity $u = 0 \text{ m/s}$, acceleration $a = 5 \text{ m/s}^2$, final velocity $v = 25 \text{ m/s}$.
Using the kinematic equation $v^2 = u^2 + 2as$:

Given: Velocity $v = 25 \text{ m/s}$, time $t = 2100 \text{ s}$.

Given: Initial velocity $u = 25 \text{ m/s}$, final velocity $v = 0 \text{ m/s}$, time $t = 25 \text{ s}$.
Using the kinematic equation $s = \frac{(u+v)}{2}t$:

Total distance $S = s_1 + s_2 + s_3$:

Convert meters to kilometers:

The distance from the village to the town is indeed $\boxed{\text{52.875 km}}$.

Distance one way = $52.875 \text{ km}$.
Total distance = $2 \times 52.875 \text{ km} = 105.75 \text{ km}$.
Convert to meters: $105.75 \text{ km} = 105.75 \times 1000 \text{ m} = 105750 \text{ m}$.

Fuel consumption rate = $0.2 \text{ litres}$ per $500 \text{ m}$.

Cost per litre = $6000 \text{ shs}$.

The cost of fuel needed is $\boxed{\text{253800 shs}}$.

c) A hydraulic brake system works based on Pascal's principle, which states that pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel.

An illustration would show:

• A brake pedal connected to a master cylinder containing brake fluid.
• Brake lines extending from the master cylinder to slave cylinders located at each wheel.
• Each slave cylinder has pistons that push brake pads against a brake disc (or brake shoes against a drum).

When the driver presses the brake pedal, a piston in the master cylinder pushes the brake fluid, creating pressure. This pressure is transmitted equally through the brake lines to the slave cylinders at the wheels. The pistons in the slave cylinders are forced outwards, pressing the brake pads against the rotating brake disc. The resulting friction slows down and stops the wheel.

d) The tyre was hot due to the conversion of kinetic energy into heat energy during braking. When the brakes are applied, friction occurs between the brake pads and the brake discs (or shoes and drums). This friction generates a significant amount of heat. This heat is then transferred to the wheel components, including the rims and, subsequently, the tyres through conduction and convection. Additionally, if there was any skidding or hard braking, direct friction between the tyres and the road surface would also generate heat in the tyres.