Question

The stopping distance ddd is the distance a vehicle will travel from the point when the brakes are fully applied to when it comes to a complete stop. A racecar with a combined mass mmm of 25 kg with the driver is traveling along a racetrack at a velocity vvv of 100 m/s. The coefficient of friction μ between wet asphalt and rubber is 0.20, while the coefficient between dry asphalt and rubber can reach 0.90. Which of the following statements is true about the stopping distance assuming friction does all the work for stopping the car?

a) Both vehicles use static friction to come to a complete stop.
b) The stopping distance is directly proportional to the initial velocity of the car.
c) The greater the coefficient of friction, the greater the stopping distance.
d) The calculated stopping distance is 4.5 times greater for a racecar on wet asphalt than on dry asphalt.

Answer 1

In physics, when a vehicle's brakes are applied, the force of friction between the tires and road surface, which depends on the coefficient of friction, stops the car. A higher coefficient of friction results in a shorter stopping distance. Therefore, the true statement about the stopping distance is that a greater coefficient of friction yields a shorter stopping distance.

Step-by-step explanation:

The question you've asked pertains to the stopping distance of a vehicle, a concept that is part of classical mechanics in physics. Specifically, it involves understanding how friction and initial velocity affect the stopping distance of a car.

When a car's brakes are fully applied, the force of friction between the tires and the road surface is what brings the car to a stop. This force of friction is determined by the coefficient of friction (μ) and the normal force, which for a car on level ground is simply its weight. A higher coefficient of friction means more frictional force and thus a shorter stopping distance.

In this scenario, since the racecar has a mass of 25 kg and is traveling at a velocity of 100 m/s, there are a few key points to answer your question:

• Static friction is what prevents the tires from sliding but once the car begins to skid, kinetic friction comes into play. Thus, statement (a) is not completely accurate.
• The stopping distance is not directly proportional to the initial velocity; it is actually proportional to the square of the velocity. Therefore, statement (b) is incorrect.
• Statement (c) is incorrect because the greater the coefficient of friction, the shorter the stopping distance due to increased frictional force.
• As for statement (d), the stopping distance on wet asphalt would indeed be longer than on dry asphalt. However, without the specific stopping distances or the exact relationship, we cannot confirm the exact multiple by which it is greater.