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Δt=6.7 s, Δx= .25 miles what is speed?

  1. Feb 1, 2013 #1
    1. The problem statement, all variables and given/known data

    A dragster starts from rest and travels 0.25 miles in 6.7 s. Assuming that the acceleration is constant, what is its speed (in miles per hour) at this point?

    Δt= 6.7 s
    Δx= .25 miles

    2. Relevant equations Constant acceleration equations

    v = vo + at

    x = xo + vo t + ½ a t2

    xo + ½ (v + vo) t

    2 a (x - xo)= v2 - vo2

    3. The attempt at a solution

    all of the relevant constant acceleration equations I have in front of me have too many variables to isolate one given this. I know I can figure Vavg .25/0.00186111 hrs (6.7 s.) = 134.3284 but this doesn't do me any good. If you could nudge me in the right direction I would appreciate it.
     
  2. jcsd
  3. Feb 1, 2013 #2
    There are only 2 things you don't know here, the acceleration and the final speed. All other things you do know. As the problem says the body starts moving from rest, so there's v0. Aside from that, you now it travels a distance of .25 miles, which all you need to now, simply define x0=0 which means Δx=x, and that's all. You should be able to solve the problem.
     
  4. Feb 1, 2013 #3
    You need to convert miles to meters. Then you'll get acceleration using x = ½at^2 (it starts from rest so v0=0). Vfinal=at
     
  5. Feb 1, 2013 #4
    so in Δr = vΔt + (1/2)a(Δt)2 the vis v0??? This was not clear. Thanks
     
  6. Feb 1, 2013 #5
    Yes. Since the car starts from rest, the equation simplifies to x = ½at^2.
     
  7. Feb 1, 2013 #6
    Yes, in that equation, the v is the inicial velocity of the body, usually named v0.
     
  8. Feb 1, 2013 #7
    Actually, you don't have to convert miles to meters.

    Also, if the acceleration is constant, then the average velocity is half the final velocity. The OP already calculated the average velocity. So.....

    Chet
     
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