Brakes are applied to a 3000-kg car moving at 30 m/s. The car skids 200 m and stops. What is the coefficient of kinetic friction?Group of answer choices4.350.1000.300.23

To find the coefficient of kinetic friction, we first need to find the deceleration of the car. We can use the equation of motion:

v^2 = u^2 + 2as

where: v = final velocity = 0 m/s (since the car stops) u = initial velocity = 30 m/s a = acceleration (which will be negative as it's deceleration) s = distance = 200 m

Rearranging the equation to find 'a', we get:

a = (v^2 - u^2) / 2s a = (0 - (30)^2) / (2*200) a = -900 / 400 a = -2.25 m/s^2

The force of friction (f) is equal to the mass (m) times acceleration (a). So, f = ma.

f = 3000 kg * -2.25 m/s^2 = -6750 N. The negative sign indicates that the force is acting in the opposite direction of motion.

The force of friction is also equal to the coefficient of friction (μ) times the normal force (N). On a flat surface, the normal force is equal to the weight of the object, which is mass (m) times gravity (g). So, N = mg.

N = 3000 kg * 9.8 m/s^2 = 29400 N.

Now we can find the coefficient of friction (μ) by rearranging the equation f = μN to solve for μ:

μ = f / N μ = -6750 N / 29400 N μ = -0.23

The negative sign simply indicates that the frictional force is acting in the opposite direction of motion. The coefficient of friction is a scalar quantity, so it doesn't have a direction. Therefore, the coefficient of kinetic friction is 0.23.