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When we integrate function of acceleration, what do we get?

  1. Nov 4, 2013 #1
    Do we get function for velocity or do we get the function for the total change in velocity?
  2. jcsd
  3. Nov 4, 2013 #2


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    What kind of integral do you mean? The "indefinite integral" is a function, the "definite integral" is a number. The "indefinite integral" of the acceleration function, [itex]\int a(t)dt[/itex] is the velocity function, v(t), plus a "constant of integration". The definite integral, [itex]\int_{t_0}^{t_1} a(t)dt= v(t_1)- v(t_0)[/itex], change in speed between times [itex]t_0[/itex] and [itex]t_1[/itex].

    We can combine the two: writing [itex]\int_{t_0}^T a(t)dt[/itex] where [itex]t_0[/itex] is a fixed time and T is a variable. It gives, for any T, the change in velocity since time [itex]t_0[/itex].
    Last edited by a moderator: Nov 4, 2013
  4. Nov 4, 2013 #3
    okay. thanks again!
  5. Nov 4, 2013 #4
    you said it tells us the change in speed.
    that means we do not get direction of change?
  6. Nov 4, 2013 #5


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    Warning: All you wrote is correct for the vector quantities [itex]\vec{v}[/itex] and [itex]\vec{a}[/itex] but in general not for the magnitudes!
  7. Nov 4, 2013 #6
    ?i don't understand.
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