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Suppose you know the acceleration of a object and the intial velocity and the position, you can use integration to calculate the linear motion.
If acceleration = a(t) and the velocity is v(t),
`a(t) = (d(v(t)))/(dt)`
`v(t) = inta(t) dt + c_1`
Also, we know,
`v(t) = (d(s(t)))/(dt)`
where s is the displacement.
`s(t) = int v(t) dt + c_2`
So you can find an expression for the displacement. Using the intial values you can find the values of the constants.
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