# The driver of the car began to brake when the car was at a distance of 200 m from the gas

The driver of the car began to brake when the car was at a distance of 200 m from the gas station and was moving at a speed of 20 m / s. What should be the force of resistance to movement so that a car weighing 1000 kg would stop at the station?

The final speed of the car is v = 0 m / s, since it is known from the condition of the problem that the driver of the car began to brake. The car at that moment was at a distance of S = 200 m from the gas station and was moving at a speed of v₀ = 20 m / s. To determine what the resistance force to motion F should be in order for a car with a mass of m = 1000 kg to stop at the station, we will use Newton’s second law:

F = m ∙ a, where a is the acceleration determined by the formula a = (v ^ 2 – v₀ ^ 2) / (2 ∙ S). Then: F = m ∙ (v ^ 2 – v₀ ^ 2) / (2 ∙ S).

Substitute the values ​​of physical quantities in the calculation formula:

F = 1000 kg ∙ (0 – (20 m / s) ^ 2) / (2 ∙ 200 m);

F = – 1000 N, the minus sign indicates that the force and acceleration are directed against the movement of the car.

Answer: the force of resistance to movement is 1000 N.

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