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1D Kinematics: Distance between 2 cars

  1. May 11, 2016 #1
    1. The problem statement, all variables and given/known data
    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?

    2. Relevant equations
    xf=xi+vo*t+(1/2)a*t2
    vf=vo+a*t

    3. The attempt at a solution
    FIrst thing I did was solve for xf.b=0+60(0.75)+(-8*.5*0.752) = 42.75ft
    Secondly, I solved for xf.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 vf=vo+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 xf=xi+vo*t+(1/2)a*t2 for each car again, getting Δxa=27.5, Δxb=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?
     
  2. jcsd
  3. May 11, 2016 #2
    pl. explain your doubts about your calculation .
     
  4. May 11, 2016 #3

    Orodruin

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    Which part are you unsure about? Your reasoning seems solid.
     
  5. May 11, 2016 #4
    Thank you for the quick reply. I feel like I was just solving things randomly, maybe it is just because this stuff is new and I don;t know exactly what I am doing yet. I wasn't confident in my approach until I got the right answer.
     
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