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How is integral calculus applied to calculate linear motion.

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How is integral calculus applied to calculate linear motion.

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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)`

Therefore,

`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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