Answer:
Step-by-step explanation:
We can use the following equations of motion to solve the problem:
v^2 = u^2 + 2as
where v is the final velocity, u is the initial velocity, a is the acceleration, s is the distance travelled.
In this case, the box is slowing down, so the initial velocity u is greater than the final velocity v. We can use a negative sign to indicate that the acceleration is opposite to the initial velocity.
Let us assume that the mass of the box is m and the coefficient of kinetic friction is μ. The force of friction acting on the box is given by f = μmg, where g is the acceleration due to gravity.
Since the acceleration of the box is 2.0 m/s^2, we have
f = ma
μmg = m(-2.0)
μg = -2.0
μ = -2.0/g
Substituting g = 9.8 m/s^2, we get
μ = -0.204
Since the coefficient of friction cannot be negative, we take the absolute value and obtain:
μ = 0.204
Therefore, the coefficient of kinetic friction between the box and the floor is approximately 0.204.