Stopping Distance and Speed Calculation Problem

What is the relationship between the stopping distance and the initial speed of a car when the brakes are applied?

Is there a formula that can help us determine the initial speed of a car based on the distance it takes to come to a stop?

Relationship between Stopping Distance and Initial Speed

When a car comes to a stop after the brakes are applied, the stopping distance is directly related to the initial speed of the car. The faster the car is traveling initially, the longer the stopping distance will be.

When a car is in motion and the brakes are applied, the kinetic energy of the car must be dissipated in order to bring the car to a complete stop. The work done by the frictional force (which is responsible for stopping the car) is directly proportional to the initial speed of the car.

To calculate the initial speed of a car based on the stopping distance, we can use the principle of work and kinetic energy. The formula to determine the relationship between the initial speed and stopping distance is:

Where: v = initial speed of the car μk = coefficient of friction between the tires and the road m = mass of the car g = acceleration due to gravity l = stopping distance

Therefore, the initial speed of the car can be determined by dividing the square root of 2 times the coefficient of friction, mass of the car, and acceleration due to gravity by the stopping distance.