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Non-Constant Acceleration Problem

  1. Apr 9, 2017 #1
    1. The problem statement, all variables and given/known data
    A new Tesla is designed that can perform a non-constant acceleration for 10 seconds of motion. The magnitude of the acceleration is given as a(t) = 1 m/s4t2

    Starting from rest, how far does the car travel over this 10 second interval?

    2. Relevant equations
    This is what is making the question difficult for me. I am unsure what equations to use with a non-constant acceleration.

    3. The attempt at a solution
    I tried solving it manipulating the constant velocity and acceleration equations, but everything I have tried has been wrong. Even if someone could point me in the right directions equations wise, I'm sure that would help me a lot.

    Thanks
     
  2. jcsd
  3. Apr 9, 2017 #2

    Ssnow

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    Hi, you can find the velocity function respect to ##t## that is ##v(t)=\int_{0}^{t} a(s)ds## and after the space ##x(t)=\int_{0}^{t}v(s)ds##, put ##t=10 s## in ##x(t)## ...
    Ssnow
     
  4. Apr 9, 2017 #3

    Ray Vickson

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    Your input is hard to read; I assume you mean ##a = k t^2,## where ##k = 1 m/s^4.##

    Anyway, you get velocity ##v## by integrating ##a## with respect to ##t##, and then you get position by integrating ##v##. No amount of manipulation of the constant-acceleration formulas can do what you need.
     
    Last edited: Apr 9, 2017
  5. Apr 9, 2017 #4
    Your assumption is correct.

    After integrating the acceleration function with respect to time, with the bounds of the integral from ##0## to ##t##, I obtained the function ##t^3/3## for the velocity. Integrating that, from 0 to t for the integral, I got ##t^4/12##, and plugging in ##t## (10 seconds), I obtained a final answer of 833.3m traveled.

    Does this all sound correct?
     
  6. Apr 9, 2017 #5

    PeroK

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    It does.
     
  7. Apr 9, 2017 #6

    Ray Vickson

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    Yes, perfect.
     
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