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Car Chase Problem

  1. Sep 23, 2007 #1
    1. The problem statement, all variables and given/known data
    Consider two cars A and B, initially side by side and both at rest. at t=0 car A begins to accelerate at a constant rate Aa, which continues for a a time Ta Until it reaches a speed Va, after which time it continues traveling at the constant speed Va. At the moment Car A reaches its cruising speed Va, car B takes off after Car A, accelerating at a constant rate Ab. at T=t* car B passes Car A.

    C.) Determine the amount of time, (Delta)t, elapsed from the moment car B begins to accelerate to the moment it passes car A. What is the velocity of car B at the moment it passes car A? Note: You may use dimensional analysis to check your answers.

    2. Relevant equations

    3. The attempt at a solution
    On a single graph i drew a Position Time Graph ... and Also i sketched a Speed-Time Graph... Me and my Roommates Have attempted to solve this problem for many hours... What can i do with the Graphs?
  2. jcsd
  3. Sep 23, 2007 #2
    On my Speed-Time Graph... the constant acceleration and constant speed of Car A will be the same distance as the constant acceleration of Car B.
  4. Sep 23, 2007 #3
    lol anyone??
  5. Sep 23, 2007 #4
    Look up my thread.... don't tell me...

    Anyway, they want you to express it algebraically. The problem is quite simple; at Ta, car A covered 1/2Aa*Ta^2. This said, you have

    1/2Aa*Ta^2 + Va*delta T = 1/2Ab*delta T^2.

    It's simply a question of isolation delta T here.
    Last edited: Sep 23, 2007
  6. Sep 23, 2007 #5
    Yes this was my formula as well.. but 1 question how come you don't use delta T for this first part of the equation ?

    is it because in the beginning ....Ta-T0...is just Ta..? ..... Ahhh I get it ...If thats right..
    Last edited: Sep 23, 2007
  7. Sep 23, 2007 #6
    Werg can u help me with the 2nd part of the problem
  8. Sep 23, 2007 #7
    So know that i got ... (delta)t= Aa*Ta^2/Ab ...
    To find the velocity when Car b passes Car A.... i used the equation ....
    X(final)-X(initial)=((Vxi+Vxf)/2) * t
    Xf-0= ((0+Vxf)/2) *t
    Xf= Vxf/2 *t
    2Xf=Vxf *t
    2Xf/t = VxF

    so i just sub My delta T in this equation?
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