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How to Find Velocity With Non-Constant Acceleration

  1. Sep 24, 2012 #1
    Hi everyone. I don't want someone to do the question so I won't include my actual homework question, but I would really appreciate if someone would tell me how to find velocity after a time t if your acceleration is non-constant and time dependent.

    For example, if your acceleration was a = 4.0t and you want to find velocity after 3.0 seconds, how would you do that? Thank you!
     
  2. jcsd
  3. Sep 24, 2012 #2

    Curious3141

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    Homework Helper

    Have you learnt calculus yet? You need to integrate the acceleration with respect to time, while setting the lower bound to 0 (seconds) and the upper bound to 3 (seconds), i.e.

    [tex]v(3) = \int_0^3 a(t) dt = \int_0^3 4t dt [/tex]

    Here, v(t) refers to velocity as a function of time, so v(3) is velocity at time 3 seconds. a(t) is acceleration as a function of time.
     
  4. Sep 24, 2012 #3
    Thanks for the answer! I know indefinite integrals but not definite so could you please explain how you solve your example? (:
     
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