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**[SOLVED] Very beginner physics 1D motion question!**

**1. Homework Statement**

Two cars move in opposite directions toward each other on a level, straight, one-lane road. When both drivers begin to brake, their front bumpers are 275 meters apart. The smaller car is initially moving at 25.0 m/s and the larger is initially moving at 30.0 m/s. The magnitude of the acceleration of the smaller car is 20.0% greater than the magnitude of the acceleration of the larger. Determine the magnitude of acceleration for each car such that when their front bumpers touch, they have just come to rest

**2. Homework Equations**

(Vf)^2=(Vi)^2+2a(Xf-Xi)

**3. The Attempt at a Solution**

TRANSLATION:

1 stands for the larger car, 2 for the smaller car...

Xi1=0 Xi2=275

Xf1=unknown Xf2=unknown Xf1=Xf2

Vi1=30 Vi2=-25

Vf1=0 Vf2=0

a1=? a2=? a2=1.2a1

EQUATE:

0=(Vi1)^2+2a1(Xf1)

0=(Vi2)^2+2.4a1(Xf2-Xi2)

To solve for a1 I isolated Xf1 in the first equation and then plugged that in where Xf2 is on the second equation, since they are equal. I ended up with:

a1=((Vi2)^2-1.2(Vi1)^2)/(2.4Xi2)

a1= ((-25)^2-1.2(30)^2)/(2.4*275)

a1=-.689 m/s^2

and therefore

a2=-.827 m/s^2

which is the magnitude if you take the absolute value....

So I am wondering if this is correct becaue I am having difficulty verifying my answers and I'm not sure if this is reasonable..