A 100kg object moving at 20 m/s comes to a stop over distance of 40 m. What is the coefficient of dynamic fiction between the object and the ground?

I tried to work it out with the formula, but I'm really confused. Please help.

To calculate the coefficient of dynamic friction between an object and the ground, we can use the equation:

F_fric = μ * m * g

where F_fric is the force of friction, μ is the coefficient of friction, m is the mass of the object, and g is the acceleration due to gravity (approximately 9.8 m/s^2).

In this case, the object comes to a stop, which means that the force of friction acts in the direction opposite to the motion of the object. Therefore, the force of friction is equal in magnitude but opposite in direction to the force that was initially moving the object.

To calculate the force that was initially moving the object, we use the equation:

F_initial = m * a

where F_initial is the initial force, m is the mass of the object, and a is the acceleration.

In this case, the initial force is equal to the product of mass and acceleration. The mass is given as 100 kg and the velocity (20 m/s) is given. Since the object stops over a distance of 40 m, we can calculate the acceleration (a) using the equation:

v^2 = u^2 + 2 * a * s

where v is the final velocity (0 m/s), u is the initial velocity (20 m/s), a is the acceleration, and s is the distance (40 m).

Rearranging the equation, we get:

0 = 20^2 + 2 * a * 40

400 = 80a

a = 5 m/s^2

Now, we can calculate the initial force using the equation:

F_initial = m * a = 100 kg * 5 m/s^2 = 500 N

Since the force of friction is equal in magnitude to the initial force but opposite in direction, F_fric = -500 N.

Substituting the known values into the equation:

-500 N = μ * 100 kg * 9.8 m/s^2

Now we can calculate the coefficient of dynamic friction (μ):

μ = (-500 N) / (100 kg * 9.8 m/s^2)

μ ≈ -0.51

The negative sign indicates that the force of friction acts opposite to the direction of motion, which is expected when an object comes to a stop.

Therefore, the coefficient of dynamic friction between the object and the ground is approximately -0.51.