Finding the distance given the intital velocity and the coefficient of friction

lenalee.9520

1. The problem statement, all variables and given/known data
A car is travelling at 15.5m/s travels on a surface where μ=0.1. The driver sees a boy run into the road 125 m ahead. She immedietly applies the brakes, locking the wheel, and skids to a stop. Where will the car be when it stops? (i.e:Will it hit the boy?)

I know I should start by figuring out the acceleration and then use

Vfinal^2=V inital^2 + 2ad

But, I am having trouble finding the acceleration.

2. Relevant equations
Fnet=ma
Ffriction= μFN
Vfinal^2=V inital^2 + 2ad


3. The attempt at a solution

tiny-tim

hi lenalee.9520! welcome to pf!

(try using the X² button just above the Reply box )
call the mass "m"

then find the force, and divide by m

(the force will be µ times … ? )

lenalee.9520

Well I ended up with

Ffriction= -mgµ

Is this correct?

tiny-tim

call the mass "m" !!

(it'll cancel out in the end)

lenalee.9520

Ffriction= -mgµ

Is what I got...
But how does it cancel out??

azizlwl

You could identify it as an energy related problem.

lenalee.9520

Well, my teacher told the class that we should only need equations from the kinematics and dynamics unit, so I've been trying to stick to those things. (I have to turn this in, so I would like to follow his instructions as much as possible, for the sake of my mark)

azizlwl

As tiny-tim said, call the mass 'm'
Then if you apply force to it, what is the acceleration?

darthfunnybot

[itex]\sum[/itex]F = ma = [itex]\mu[/itex]_kmg
Once you solve for the acceleration, the rest is just a 'timeless' kinematics problem.
V_f² = 0 = V_o² + 2aΔx

tiny-tim

acceleration = F_friction/m ?