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**1. Homework Statement**

A car hits another car at rest. Debris is found 6.75m from the cars, the two cars stuck together over a distance of 6.75m, there are skid marks a distance of 312m before the car crash, car 1=2946kg, car2=1232kg, coefficent of friction is .72. Find the initial velocity of car 1.

**2. Homework Equations**

W=ΔKE=KEf-KEi=fd

m1v1=(m1+m2)v2

**3. The Attempt at a Solution**

I assumed the distance after the collision is 6.75m, and the distance before it is 312m.

First I tried to solve for the speed when the cars hit using the work-energy theorem

W=ΔKE=KEf-KEi, KEf=0

KEi=-1/2mv

^{2}

W=fd, W=Ff(d), W=(mg)(coefficient of static friction)(d)=-1/2mv

^{2}

(2946+1232)(.72)(6.75)(9.81)=1/2(2946+1232)(v

^{2}), v=9.76m/s

Then I used that answer in the conservation of momentum equation

m1v1=(m1+m2)v2

2946v1=4178(9.76)

v1=13.85ms=30.98mph

I'm not completely sure what I was supposed to use for my force, since the car was already in motion, but no forces were acting on the car besides friction.I feel like I messed up the part in the work-energy theorem. I ended up not using the stopping distance for car 1 and I think my answer should be greater, but I'm not sure.

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