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Acceleration straight line graph

  1. May 14, 2013 #1
    1. The problem statement, all variables and given/known data
    A particle starts from rest and accelerates as shown in the attached figure. Determine (a) the article's speed at t=10s and t=20s. (b) The distance traveled in the first 20s.


    2. Relevant equations

    a=dv/dt

    3. The attempt at a solution
    (a) t=10s, speed = 20m/s
    t=20s, speed = 5m/s
    Those were obtained by taking the area under the acceleration.

    (b) book gives the answer 262m. NO idea how this came about. I thought about 225m being the answer since 20m/s * 10s + 5m/s * 5s, but this wouldn't be correct because the velocity is changing, not constant. Any help would be appreciated.
     

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  3. May 14, 2013 #2
    You can use the constant-acceleration equations to work this out.
     
  4. May 14, 2013 #3
    k is there a way by the graph or integration? I want to use something that's always going to work, if that's possible.
     
  5. May 14, 2013 #4

    SteamKing

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    Graphically, the change in velocity from t1 to t2 represents the area under the acceleration curve.

    After constructing a velocity curve, the change in displacement is the area under the velocity curve.

    If the acceleration curve is positive, how does that affect velocity?
    If the acceleration curve is negative, how does that affect velocity?
    If the acceleration curve is zero, how does that affect velocity?
     
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