A car weighing 300 kg moves at a speed of 36 km / h. When the brakes are applied, a force of 2000N

A car weighing 300 kg moves at a speed of 36 km / h. When the brakes are applied, a force of 2000N is applied. What is the distance of the applied brakes to a complete stop?

When the brakes are applied to a car with a mass of m = 300 kg, a force F = – 2000 N acts. The “minus” sign means that the acting force and acceleration have a direction opposite to the speed of the car.

According to Newton’s second law, the force is determined by the formula:

F = m ∙ a, where a is the braking acceleration caused by this force. We get:

a = F: m.

Since the car moves with the brakes on until it stops completely, that is, its final speed will be v = 0 m / s, then to determine the distance traveled, we use the formula to determine the path S with uniformly accelerated movement:

S = (v ^ 2 – v₀ ^ 2): (2 ∙ a), or S = – v₀ ^ 2: (2 ∙ F: m);

S = – (m ∙ v₀ ^ 2): (2 ∙ F).

From the condition of the problem it is known that the car is moving at a speed v₀ = 36 km / h = 10 m / s, we get:

S = – (300 kg ∙ (10 m / s) ^ 2): (2 ∙ (- 2000 N));

S = 7.5 m.

Answer: the braking distance will be 7.5 m.