a car travels with velocity along a straight horizontal road . if the coefficient of static friction between the tyres and the road is us . find the shortest distance travelled by the car before it stop

All your numbers are missing, but just find the net force and then use

F = ma
v = at
s = 1/2 at^2

But how to find net force if all numbers are missing?

To find the shortest distance traveled by the car before it stops, we need to consider the forces acting on the car.

When the car is moving, the static friction between the tires and the road provides the necessary force to overcome the opposing forces. The maximum static friction force can be calculated using the equation:

Fs ≤ us * N,

where Fs is the static friction force, us is the coefficient of static friction, and N is the normal force exerted by the road on the car.

However, when the car reaches its maximum stopping potential, the static friction force is at its maximum value, and the opposing force (usually the force of kinetic friction) overcomes it, causing the car to stop.

The formula for the opposing kinetic friction force is:

Fk = uk * N,

where Fk is the kinetic friction force and uk is the coefficient of kinetic friction. Since the car comes to a stop, Fk equals the maximum static friction force.

Setting Fs = Fk, we can write:

us * N = uk * N.

Simplifying the equation, we find:

us = uk.

Therefore, the coefficient of static friction us is equal to the coefficient of kinetic friction uk.

Knowing this, we can calculate the shortest distance traveled by the car before coming to a stop using the equation:

d = vi^2 / (2 * uk * g),

where d is the distance traveled, vi is the initial velocity of the car, uk is the coefficient of kinetic friction, and g is the acceleration due to gravity.

Substituting equal values of us for uk, the equation becomes:

d = vi^2 / (2 * us * g).

So, to find the shortest distance traveled by the car before it stops:

1. Determine the coefficient of static friction.
2. Calculate the shortest distance using the formula d = vi^2 / (2 * us * g), where vi is the initial velocity of the car.

Note: Be sure to use consistent units for all quantities involved in the calculation.