Determine the coefficient of friction

[retracell]

Homework Statement

A small 10kg cardboard box is thrown across a level floor. It slides a distance of 6.0m, stopping in 2.2s. Determine the coefficient of friction between the box and the floor.

Homework Equations

$$\[\Delta d={{v}_{0}}t+\frac{1}{2}a{{t}^{2}}\]$$
$$\[{{F}_{net}}=ma\]$$

The Attempt at a Solution

$$\[ma=-\mu mg\]$$
$$\[10a=-\mu 10(9.8)\]$$

$$\[6={{v}_{0}}(2.2)-\frac{1}{2}a{{(2.2)}^{2}}\]$$

How would I go about finding the acceleration?
The answer given is 0.26, which means the initially velocity of the cardboard box is zero. Is it okay to assume that the box is initially going at zero velocity and then decelerates to zero velocity due to friction?

 

[radou]

Write down the equation for the velocity of the box. What can you conclude from it? Since the box is thrown, obviously the initial velocity can't be zero.

 

[inutard]

One more equation to use is vf = vi+at, thus,
-vi = at
since vf = 0.
Now there are two equation with two unknowns (when considering the equations you have posed). You may now solve for acceleration.