Horizontal escape lanes made of loose gravel have been constructed at the side of some roads on steep hills so that vehicles can stop safely when their brakes fail - AQA - A-Level Physics - Question 1 - 2018 - Paper 1

To determine if an 85 m lane is sufficient, we need to calculate the distance required to stop the vehicle. Using the formula for distance under uniform acceleration: $d = v_i t + \frac{1}{2} a t^2$

Where:

• $v_i = 20 \, \text{m/s}$ (initial speed)
• $a = -5 \, \text{m/s}^2$ (deceleration)
• $t = 2 \, \text{s}$ (time taken to stop)

Calculating: $d = 20 \cdot 2 + \frac{1}{2} \cdot (-5) \cdot (2)^2$ $d = 40 - 10 = 30 \, \text{m}$

Thus, for the vehicle to stop is 30 m, an 85 m lane is sufficient to stop the vehicle.

When a vehicle is decelerated, its kinetic energy is converted to other forms of energy. Initially, the vehicle possesses kinetic energy given by: $KE = \frac{1}{2} mv^2$

As the vehicle decelerates, this kinetic energy is transformed primarily into:

1. Heat Energy: Through friction between the tires and the gravel, generating heat.
2. Potential Energy: If in a sloped escape lane, the vehicle's energy may convert to gravitational potential energy as it climbs.
3. Sound Energy: From the noise of tires against gravel, dissipating energy into the environment.

This energy transformation illustrates the conservation of energy principle.

Calculate the deceleration and stopping distance for the ramp scenario. First, determine the vertical height using trigonometry: $h = 85 \cdot \sin(25^") \approx 35.4 \, \text{m}$

Apply the same stopping distance formula: Using:

• $v_i = 20 \, \text{m/s}$
• Assume similar deceleration as gravel, say $-5 \, \text{m/s}^2$ (idealized)

Distance required to stop: $d_{ramp} = 20 \cdot 2 + \frac{1}{2} \cdot (-5) \cdot (2^2) = 30 \, \text{m}$

Since $85 \, \text{m} > 30 \, \text{m}$, the ramp is sufficient to stop the vehicle.

An escape lane with gravel generally offers better traction, but may lead to longer stopping distances compared to a ramp. The ramp, however, allows for controlled deceleration while utilizing gravitational potential energy effectively.

In terms of safety:

• Gravel: Increases risk due to potential for skidding but offers higher stopping power.
• Ramp: Aids in effective deceleration, but requires precise angle and surface quality to minimize slipping.

Overall, while both can be effective, a well-designed ramp could offer a more controlled and potentially safer experience compared to gravel.