Finding Initial Speed of Car Skidding to a Stop on Wet Road

[Packocrayons]

Homework Statement

The driver of a car is traveling on a wet, level road, and slams on the brakes. The car slides 88M to a stop, with a coefficient of friction of 0.42. What was the initial speed of the car?

Homework Equations

KE = .5mv²
Δd = v₁Δt + .5aΔt²
Any other kinematics, dynamics, and work/energy/power equations.

The Attempt at a Solution

I have tried subbing equations together but I always end up with 3 variables, v₁, a, and Δt. I feel like mass is required for any solution, because then friction could be calculated and the rest would be simple.

 

[SHISHKABOB]

well so there's only one force acting on the car during this time, and that's the force due to friction. Try and get the acceleration of the car from that.

 

[Packocrayons]

But you can't find the force of friction without the normal force (requiring mass), and if you wanted to find acceleration you would need time, correct?

 

[SHISHKABOB]

Use Newton's second law of motion and the definition of the force of friction.

 

[Packocrayons]

How would I use that, Fnet=ma doesn't really help as I have none of those values.

 

[SHISHKABOB]

Well you know that the only force acting on the car is the force due to friction, this is

F_fric = μF_N = μmg

and you know that the sum of all the forces acting on something is

F_net = ma

what can you get from that?

 

[Packocrayons]

My brain is telling me:
μg = a
But I have the strangest feeling that's wrong.
Thanks for the help by the way.

 

[SHISHKABOB]

your brain is correct :)

Since we know that F_net = ma and that F_fric is the only force acting on the car and we also know that F_net = F_fric

we can therefore say that ma = μmg

and therefore a = μg

from that you can use one of the basic equations of constant acceleration.

 

[Packocrayons]

Thanks, I understand how to do the problem now, and that should help me with other ones.