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

[lenalee.9520]

Homework Statement

A car is traveling 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.

Homework Equations

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

The Attempt at a Solution

 

[tiny-tim]

welcome to pf!

hi lenalee.9520! welcome to pf!

(try using the X² button just above the Reply box )

… But, I am having trouble finding the acceleration.

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]

You should identify it as an energy related problem.

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]

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

 

[tiny-tim]

Ffriction= -mgµ

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

acceleration = F_friction/m ?