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Shouldn't these equations produce the same result?

  1. Oct 1, 2015 #1
    1. The problem statement, all variables and given/known data
    If a pilot accelerates at more than 4g, he begins to “gray out” but doesn’t completely lose consciousness. (a) Assuming constant acceleration, what is the shortest time that a jet pilot starting from rest can take to reach Mach 4 (four times the speed of sound) without graying out? (b) How far would the plane travel during this period of acceleration? (Use 331 m s for the speed of sound in cold air.)

    2. Relevant equations
    2aΔx=V2-V02
    Δx=V0t+(1/2)at2

    3. The attempt at a solution
    I was reviewing my work for the chapter and came across a problem with part b. I used 2aΔx=V2-V02 instead of Δx=V0t+(1/2)at2 like I did the first time. The time it takes is 33.7 seconds, and initial velocity is zero with final velocity being 1324 m/s. The acceleration is 39.24 m/s2. Using the second equation, I get the right answer of 22392 m. But using the first equation, I get 2087 m. Why is this? If there is a final velocity and an initial velocity, and acceleration is the same with both, wouldn't it have to take the same time?
     
  2. jcsd
  3. Oct 1, 2015 #2

    ehild

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    Gold Member

    You certainly miscalculated something. Both method gives the same result.
     
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