A 1000-kg car comes to a stop without skidding. The car's brakes do 50,000 J of work to stop the car. What was the car's velocity when the brakes were initially applied?

To find the car's initial velocity when the brakes were applied, we can use the work-energy principle. The work done by the brakes is equal to the change in kinetic energy of the car. Using the given information on the work done by the brakes, we can calculate the initial velocity of the car.

Explanation:

To find the car's initial velocity when the brakes were applied, we can use the work-energy principle. The work done by the brakes is equal to the change in kinetic energy of the car. The work done is equal to the force applied (which is the friction force between the brakes and the car) multiplied by the distance over which the force is applied.

The force of friction can be calculated using the equation F = μk Mcg, where μk is the coefficient of kinetic friction, Mc is the mass of the car, and g is the acceleration due to gravity. The distance over which the force is applied can be determined from the given work done by the brakes.

Once we have the force of friction and the distance, we can use the work-energy principle to find the initial kinetic energy of the car. Since the car comes to a stop, its final kinetic energy is zero. From the initial and final kinetic energies, we can calculate the initial velocity of the car.

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