# When the brakes of a car moving at 40 m/s are pressed, it takes 32 m to come to a stop. What is the coefficient of kinetic friction. Why is the mass of the car not required here.

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The car is moving at 40 m/s when the brakes are pressed. It takes 32 m to come to a stop. The speed of the car when it comes to a stop is 0 m/s.

The kinetic energy of a moving object is given by (1/2)*m*v^2. Let the mass of the car be m.

Initially its kinetic energy was (1/2)*m*40^2. The final kinetic energy is 0. This change in kinetic energy is due to work done by a resistive force acting in a direction opposite to the direction in which the car is moving. The force of kinetic friction is given as the product of the normal force N and the coefficient of kinetic friction k, F = k*N. The work done by the force of friction is is k*N*d . The normal force of the car is m*g

Here we have (1/2)m*40^2 - 0 = k*m*g*d

The mass m is not required here as it gets canceled.

This gives:

(1/2)*40^2 = k*9.8*32

=> k = 1600/2*9.8*3.2

=> k = 25.51

This is truly a very high coefficient of kinetic friction.

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