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Nonuniform Linear Acceleration

  1. Jul 10, 2016 #1
    1. The problem statement, all variables and given/known data
    Refer to figure.

    2. Relevant equations
    v=ds/dt → ds=vdt
    a=dv/dt → dv=adt
    ads=vdv

    3. The attempt at a solution
    I tried taking the derivative of the given position function. Then I am kind of lost from there.
     

    Attached Files:

  2. jcsd
  3. Jul 10, 2016 #2
    First, you must find velocity equation: v=ds/dt=f(t)
    After that v=40m/s then f(t)=v=> t0
    Finally, find aceleraition equation: a=dv/dt =g(t)
    Replace the t0 a(t0)=g(t0)
     
  4. Jul 10, 2016 #3
    If you do this then you don't get the solution that was provided...
     
  5. Jul 10, 2016 #4
    Ah two time are different. It is the time that you find aceleration
    Find the time from v=15 to v=75
    From v(t) equation: f(t1)=15m/s => t1
    f(t2)=75m/s => t2 So the time is t2-t1
     
  6. Jul 10, 2016 #5

    cnh1995

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    If initial velocity is the velocity at t=0, it is not 15m/s. If you neglect the 15m/s, your answers will match the given answers.
     
  7. Jul 11, 2016 #6

    haruspex

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    Seems to me you get the given answers by taking the initial speed as 15m/s and changing the displacement to be 3t3+15t+6 to match.
     
  8. Jul 11, 2016 #7

    cnh1995

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    Right.. I meant to say neglect 14m/s and take initial velocity as 15m/s. I was about to edit but my network went off and later when I signed up again, I totally forgot that I was going to edit the post. Thanks!
     
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