Answer :
The statement being true when the car is slowing down due to the application of the brakes is : The brakes do negative work on the car.
The correct answer is option A.
When a car is slowing down due to the application of the brakes, the brakes apply a force of friction in the opposite direction to the car's motion. According to the work-energy principle, work is done when a force acts on an object and displaces it. The work done by a force is given by the equation:
Work = Force × Displacement × cos(θ)
In this case, the force applied by the brakes is in the opposite direction to the displacement of the car, resulting in an angle of 180 degrees. Since the cosine of 180 degrees is -1, the work done by the brakes is negative.
Negative work means that energy is being transferred from the car to the brakes. The frictional force of the brakes converts the kinetic energy of the moving car into other forms of energy, such as heat and sound. This causes the car to slow down and ultimately come to a stop.
It's important to note that work is a scalar quantity, meaning it only has magnitude and no direction. Therefore, the negative sign indicates the transfer of energy in the opposite direction of the displacement.
Option B, stating that the brakes do no work on the car, is incorrect because work is indeed being done by the brakes to slow down the car.
Option C, suggesting that the brakes can do positive or negative work depending on the car's direction, is incorrect because the work done by the brakes is consistently negative regardless of the car's direction.
Option D, stating that the brakes do positive work on the car, is incorrect based on the explanation above. The brakes do negative work by transferring energy from the car to the braking system.
Therefore, from the given options the correct one is option A.
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