Determine the minimum braking distance of a car on a horizontal section of the highway at an initial

Determine the minimum braking distance of a car on a horizontal section of the highway at an initial speed of 36 km / h, if the maximum value of the coefficient of friction at rest of tires on the highway is 0.55.

Given:

v = 36 km / h = 10 m / s – initial vehicle speed when braking;

k = 0.55 – coefficient of friction;

g = 10 m / s ^ 2 – acceleration of gravity.

It is required to determine the braking distance of the vehicle S (meters).

According to Newton’s second law:

Ftr = m * a – during braking, only frictional force imparts acceleration to the car.

k * m * g = m * a;

a = k * g = 0.55 * 10 = 5.5 m / s ^ 2 – the acceleration with which the car brakes.

S = v ^ 2/2 * a = 10 ^ 2/2 * 5.5 = 100/11 = 9 meters.

Answer: the braking distance of the car will be 9 meters.