Car Coming to a Stop w/ Kinetic Energy and Friction

[logan3]

Homework Statement

An 1100-kg car traveling at 24 m/s coasts through some wet mud in which the net horizontal resistive force exerted on the car from all causes (mostly the force exerted by the mud) is 1.7 x 10^4 N. Determine the car’s speed as it leaves the 18-m-long patch of mud.

m = 1,100 kg
v_i = 24 m/s
\vec F = -1.7x10^4 N
\vec s = 18 m

Homework Equations

KE_i = \frac {1}{2} mv_i^2
\Delta KE = \vec F \vec s
\Delta KE = KE_f - KE_i \Rightarrow KE_f = \Delta KE + KE_i \Rightarrow \frac {1}{2} mv_f^2 = \Delta KE + KE_i
\Rightarrow v_f = \sqrt {\frac {2(\Delta KE + KE_i)}{m}}

The Attempt at a Solution

KE_i = \frac {1}{2} (1,100 kg)(24 m/s)^2 = 316,800 J
\Delta KE = (-1.7x10^4 N)(18 m) = -306,000 J
\Rightarrow v_f = \sqrt {\frac {2((-306,000 J) + (316,800))}{(1,100 kg)}} = 4.4312 m/s \sim 4.4 m/s

Thank-you

 

[NascentOxygen]

That looks right.

And it means the title of this thread is a bit misleading.