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## Homework Statement

Car A is traveling a distance

*d*behind Car B. Initically both cars are traveling at the same speed of 60 ft/s. Suddenly Car B applies the brakes, causing Car B to decelerate at 8ft/s2. It takes the driver of Car A 0.75 seconds to react, and when she applies her brakes Car A decelerates at 20ft/s2.

What is the initial minimum distance d between the cars so as to avoid a collision?

## Homework Equations

x

_{f}=x

_{i}+v

_{o}*t+(1/2)a*t

^{2}

v

_{f}=v

_{o}+a*t

## The Attempt at a Solution

FIrst thing I did was solve for x

_{f.b}=0+60(0.75)+(-8*.5*0.75

^{2}) = 42.75ft

Secondly, I solved for x

_{f.a}=0+60(0.75) = 45ft

So I know after 0.75 seconds, the distance d = c+2.25. Now I need to solve for c.

I know that A will continually get closer to B until their velocities are equal again so I then set v

_{f}=v

_{o}+a*t equal to each other for each car (once I found final velocity of B after 0.75 seconds) and solved for t, which was 0.5 seconds.

After that I solved x

_{f}=x

_{i}+v

_{o}*t+(1/2)a*t

^{2}for each car again, getting Δx

_{a}=27.5, Δx

_{b}=26. 27.5-26 = c, which i then substituted in d = c + 2.25 to get the answer.

I got the right answer, but I am really unsure about the process. I thought my way through it but it was really roundabout. Is there a more logical process to solving this?