A car is traveling at 44.4 km/hr on flat highway. If the coefficient of friction between road and tires on a rainy day is 0.114, what is the minimum distance in which the car will stop?

Vf^2=Vi^2+2ad bit a=forcefricion/mass or

a=mu*mg/m=mu*g

solve for d.
change velocity to m/s

To find the minimum stopping distance of the car, we need to consider the force of friction acting between the tires and the road. The force of friction can be calculated using the equation:

Force of friction = coefficient of friction * normal force

The normal force is equal to the weight of the car, which can be calculated using the equation:

Weight = mass * gravitational acceleration

Assuming the car's mass is m, and the gravitational acceleration is 9.8 m/s^2, the normal force is given by:

Normal force = m * 9.8

Now, the force of friction can be given as:

Force of friction = 0.114 * (m * 9.8)

The force of friction is responsible for slowing down the car, and it opposes the motion. Therefore, it acts in the opposite direction of the car's velocity.

In this case, the force decelerating the car is the force of friction. The deceleration can be calculated using Newton's second law of motion:

Force = mass * acceleration

Since the force acting on the car is the force of friction, we can substitute the equation for force of friction into Newton's second law:

0.114 * (m * 9.8) = m * a

Simplifying the equation, we get:

1.1152 * m = m * a

Dividing both sides by m, we get:

1.1152 = a

This means that the acceleration of the car is equal to 1.1152 m/s^2.

Now, we can calculate the stopping distance using the equations of motion. Since the car is initially traveling at 44.4 km/hr, which is equivalent to 12.3 m/s, and it comes to a stop, the final velocity, v=0.

The equation to calculate the stopping distance is:

Stopping distance = (initial velocity^2) / (2 * acceleration)

Substituting the values, we get:

Stopping distance = (12.3^2) / (2 * 1.1152)

Calculating this, we find:

Stopping distance ≈ 67.6 meters

Therefore, the minimum stopping distance for the car in this scenario is approximately 67.6 meters.