In what distance can a 1500kg automobile be stopped if the brake is applied when the speed is 20m/s and the coefficient of sliding friction is 0.7 between the tyres and the ground? i need a full step by step explanation

1) The braking force is provided by the frictional force, which is given by:

where

is the coefficient of friction

m=1500 kg is the mass of the car

is the gravitational acceleration

Substituting numbers into the equation, we find

2) The work done by the frictional force to stop the car is equal to the product between the force and the distance d:

(1)

where we put a negative sign because the force is in the opposite direction of the motion of the car.

3) For the work-energy theorem, the work done by the frictional force is equal to the variation of kinetic energy of the car:

(2)

The final kinetic energy is zero, so the variation of kinetic energy is just equal to the initial kinetic energy of the car:

4) By equalizing eq. (1) and (2), we find the distance, d: