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Physics- velocity/ distance problem?

  1. Sep 13, 2010 #1
    1. The problem statement, all variables and given/known data

    An object starts from rest and has an acceleration given by
    a = Bt^2 − 1/2Ct, where B = 4.5 m/s^4 and C = −2.2 m/s^3

    (1) What is the object's velocity after 7.5 s? (Indicate the direction with the sign of your answer.)

    (2) How far has the object moved after t = 7.5 s?


    2. Relevant equations

    v=at


    3. The attempt at a solution

    I integrated the equation its not coming out right

    what am i doing wrong?

    If someone can kindly explain.

    Here is the attachment
     

    Attached Files:

    Last edited: Sep 13, 2010
  2. jcsd
  3. Sep 13, 2010 #2
    Hint
    v=at is valid if acceleration is not time dependent (i.e. it is constant)
     
  4. Sep 13, 2010 #3
    So, I am using the wrong equation? What equation should i use?
     
  5. Sep 13, 2010 #4
    you have to integrate the equation not differentiate
     
  6. Sep 13, 2010 #5
    So i have to integrate a= Bt^2- 1/2Ct?

    Do i substitute the answer in equation v=at? Or i cant use that equation at all since a is time dependent.

    Can you show some work so I have a better idea?
     
    Last edited: Sep 13, 2010
  7. Sep 13, 2010 #6
    We derive the equation v=u+at assuming that acceleration is constant.
    here acceleration is time dependent
    dv/dt = a
    dv=adt
    substitute a with the equation you have
    integrate both sides of the equation with limits 0 to v and 0 to t respectively
    after this you get an equation of v as a funtion of time.
    substitute t=7.5s in this equation to get velocity at that time.
     
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