Calculating distance from acceleration equation.

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I need to calculate the distance travelled from an acceleration time equation. I know that integrating the acceleration equation will give me the velocity and integrating that will give the displacement. How should I get distance?

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You can just take the integral of the absolute value of velocity over time, or the magnitude if more generally it's a vector. Intuitively that's because you add up all the little distances travelled in each time step, regardless of direction to get distance.