The braking force of a moving vehicle opposes the force of the the vehicle's forward movement. The braking force decelerates the vehicle, which comes to a complete stop once the brakes have done an amount of work equal to the motion's kinetic energy. You can therefore calculate a vehicle's kinetic energy and associated speed from the braking force and the distance over which the vehicle stops. A vehicle's kinetic energy is equal to half the product of its mass and the square of its speed.
Multiply the braking force by the distance the vehicle travels as it brakes. For this example, imagine a force of 6,000 Newtons and a vehicle that brakes over 100 meters: 6,000 --- 100 = 600,000. This is the work that the brakes perform and the vehicle's initial kinetic energy.
Divide the result by 0.5, because the body's kinetic energy is half the product of its mass and the square of its velocity: 600,000 ÷ 0.5 = 1,200,000 joules.
Divide this answer by the vehicle's mass. If it weighs, for instance, 2,000 kg:
1,200,000 ÷ 2,000 = 600.square meters per second squared.
Find the square root of this answer: 600^0.5 = 24.5 meters per second. This is the vehicle's speed.
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