Solving Friction Problem 3: Initial Velocity of Object

[-Physician]

Homework Statement

An object takes 12.3 meters to stop because of friction. Assume no skidding. If the coefficient of static friction is 0.5, what is the initial velocity of the object?




2. The attempt at a solution
My teacher said that in this task the mass doesn't matter, so we would have
$F_{net}=ma$
$F-ug=a$
The object is on motion and we need to find v₀ so we would have
$v_0^2=v_f^2-2ax$.
Now for this we need the acceleration, so
$a=F-ug$, I have the coefficient and the gravity, but no applying force, so how can I find the acceleration, and how will I find the v₀, If I have no acceleration?

 

[genericusrnme]

Do you know about the work/energy relation?
If you do this problem becomes a lot simpler.

Regarding your attempt;
What is this F you have in your force equation
F-ug=a
From the conditions given I don't see what other external force is being applied other than that friction.

 

[-Physician]

Sorry for double posting I think I got it:
In this case the force of friction is the net force so (thanks to genericusrnme)
$ug=a$
$=0.5(9.81\frac{m}{s^2})=a$
$4.905\frac{m}{s^2}=a$
$v_0^2=v^2-2ax$
$v_0^2=0\frac{m^2}{s^2} - 2(4.905\frac{m}{s^2})(12.3m)$
$v_0^2=-120.663\frac{m}{s}$ (to the left)
$v_0=\sqrt{120.663}$
$v_0=10.98467113754436\frac{m}{s}$
Is that right?

 

[genericusrnme]

Yes, that is correct