How Far Will a Box Slide on a Frictional Surface After Being Pushed?

[Arbitrary]

In preparing for a test I came across this problem:

A box is given a push so that it slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.2 and the push imparts an initial speed of 3.0m/s?

Here's what I've come up with so far:

Fapplied - Ffriction = ma

V0=3, x=?, a=?, Vf=0
Vf^2=Vo^2+2ax;
0=3^2+2ax
-9=2ax

I can't come up with any more equations, and there are currently too many variables to put the equations together. It seems pretty straightforward--perhaps I'm just missing something crucial.

 

[Rozenwyn]

*edit
Opps, nvm. :p

 

[kyle8921]

I would first start by clarifying the question and defining all the variables involved. In this case, the variables are the force applied (Fapplied), the coefficient of kinetic friction (μk), the initial speed (V0), the distance traveled (x), the acceleration (a), and the final speed (Vf).

Next, I would use the given information to calculate the force of friction (Ffriction) using the equation Ffriction = μk * m * g, where m is the mass of the box and g is the acceleration due to gravity.

Then, I would use the given initial speed and the calculated force of friction to solve for the acceleration using the equation Fapplied - Ffriction = ma.

Once the acceleration is known, I would use the equation Vf^2 = V0^2 + 2ax to solve for the distance traveled (x).

It is important to keep track of units throughout the calculations to ensure the final answer is in the correct unit (in this case, meters).

In conclusion, the distance the box will travel can be calculated by first determining the force of friction, then solving for the acceleration, and finally using the equation for distance traveled to find the answer. It is important to carefully define and track all variables and units to ensure an accurate solution.