1. Understand the Forces:

* Gravity (mg): Acts downwards.

* Normal Force (N): Acts upwards, equal in magnitude to the gravitational force to keep the block from sinking into the surface.

* Friction (f): Acts opposite to the direction of motion, slowing the block down.

2. Apply Newton's Second Law:

* Sum of forces = mass * acceleration

Since the block is moving horizontally, we'll focus on the forces in the horizontal direction. The only force acting horizontally is friction.

* f = ma

3. Relate Friction to the Coefficient of Kinetic Friction:

* f = μkN

* μk is the coefficient of kinetic friction

* N is the normal force (equal to mg in this case)

4. Use Kinematics to Find Acceleration:

* We know the initial velocity (vi = 1.4 m/s), the final velocity (vf = 0 m/s), and the time (t = 0.80 s). We can use the following kinematic equation to find the acceleration:

* vf = vi + at

5. Solve for the Coefficient of Kinetic Friction:

a. Find acceleration:

* 0 = 1.4 m/s + a(0.80 s)

* a = -1.75 m/s² (negative because the block is decelerating)

b. Find the force of friction:

* f = ma = (0.300 kg)(-1.75 m/s²) = -0.525 N

c. Find the coefficient of kinetic friction:

* f = μkN

* -0.525 N = μk (0.300 kg)(9.8 m/s²)

* μk = -0.525 N / (0.300 kg)(9.8 m/s²)

* μk ≈ 0.18

Therefore, the coefficient of kinetic friction is approximately 0.18.