An object slides on a level surface in the +x direction. It slows and comes to a stop with a constant acceleration of -2.45 m/s2. What is the coefficient of kinetic friction between the object and the floor? (please include explanation)

u = a/g.

For a detailed explanation, see Related Questions: Sat, 11-17-12, 5:33 PM.

To find the coefficient of kinetic friction between the object and the floor, we can use the equations of motion.

First, let's identify the given information:
- Initial velocity (u) = 0 m/s (since the object comes to a stop)
- Acceleration (a) = -2.45 m/s^2 (the negative sign indicates that the object is slowing down)
- Final velocity (v) = unknown
- Displacement (s) = unknown
- Coefficient of kinetic friction (μ) = unknown

We'll use the kinematic equation that relates initial velocity, final velocity, acceleration, and displacement:
v^2 = u^2 + 2as

Since the object comes to a stop, the final velocity (v) is 0. Plugging in the values, we have:
0^2 = (0)^2 + 2(-2.45)s

Simplifying the equation gives:
0 = -4.9s

From here, we can see that the displacement, s, must be 0. If there is no displacement, it means that there is no work done against friction in stopping the object. In other words, the friction force is zero.

The friction force can be determined using the equation:
Friction force (f) = coefficient of kinetic friction (μ) * normal force (N)

Since the object is on a level surface, the normal force (N) is equal to the weight (mg), where m is the mass of the object and g is the acceleration due to gravity.

Since the friction force is zero, we have:
0 = μ * (mg)

To find the coefficient of kinetic friction (μ), we divide both sides by (mg):
0 = μ

Therefore, the coefficient of kinetic friction between the object and the floor is zero, indicating that there is no friction between them.