A car is travelling at 42.4 km/h on a flat highway. The acceleration of gravity is 9.81 m/s^2. If the coefficient of friction between the road and the tires on a rainy day is 0.125 what is the minimum distance for the car to stop? Answer is metres

First, convert speed (V) to units of m/s.

42.4 km/h = 11.78 m/s

Initial kinetic energy = Work done against friction

(1/2)MV^2 = M*g*Uk*X

M cancels out.

X = V^2/(2*g*Uk) is the stopping distance, if the car is skidding.

If the brakes manage to apply the maximum force that prevents a skid as an automatc braking system (ABS) is supposed to do, the static friction coefficient Us can be used instead of Uk, the kinetic friction coefficient. In that case you get a minimum stopping distance.

They don't say which friction coefficient they are providing.

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

force of friction = coefficient of friction * normal force

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

weight = mass * acceleration due to gravity

So, let's break down the problem step by step:

Step 1: Convert the car's speed to meters per second (m/s):
Given that the car is traveling at 42.4 km/h, we need to convert this to m/s. To do this, we multiply the speed by (1000 m / 1 km) and divide by (3600 s / 1 h):
42.4 km/h = (42.4 * 1000) / 3600 = 11.78 m/s

Step 2: Determine the normal force acting on the car:
To calculate the normal force, we need to know the mass of the car. Let's assume it's 1000 kg:
weight = mass * acceleration due to gravity = 1000 kg * 9.81 m/s^2 = 9810 N

Step 3: Calculate the force of friction acting on the car:
force of friction = coefficient of friction * normal force = 0.125 * 9810 N = 1226.25 N

Step 4: Calculate the deceleration of the car:
By using Newton's second law, we know that force = mass * acceleration. In this case, the force of friction is acting in the opposite direction of motion, so it is a decelerating force. So, we can write:
force of friction = mass * acceleration
1226.25 N = 1000 kg * acceleration
acceleration = 1226.25 N / 1000 kg = 1.22625 m/s^2

Step 5: Calculate the minimum stopping distance:
We can use the kinematic equation:
v^2 = u^2 + 2as
where v is the final velocity (which is 0 m/s since the car stops), u is the initial velocity (11.78 m/s), a is the acceleration (-1.22625 m/s^2), and s is the stopping distance (what we want to find).

Rearranging the equation, we have:
s = (v^2 - u^2) / (2 * a)
s = (0^2 - 11.78^2) / (2 * (-1.22625))
s = 142.86 m

Therefore, the minimum stopping distance for the car is approximately 142.86 meters.