$\"\"$

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Velocity of a particle is $\"\"$ meters per second, where $\"\"$ is time in seconds.

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Displacement is the anti derivative of velocity function.

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$\"\"$ .

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$\"\"$ .

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Integration by parts formula : $\"\"$ .

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Assume $\"\"$ and $\"\"$ .

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Consider $\"\"$ .

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Differentiate on each side.

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$\"\"$ .

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$\"\"$ .

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Integrate on each side.

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$

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Consider $\"\"$ .

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Assume $\"\"$ and $\"\"$ .

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Consider $\"\"$ .

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Differentiate on each side.

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$\"\"$ .

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$\"\"$ .

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Integrate on each side.

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$\"\"$

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$\"\"$ .

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$\"\"$

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Substitute equation (2) in equation (1).

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$\"\"$

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Therefore $\"\"$ $\"\"$ .

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The distance travel during the first $\"\"$ seconds $\"\"$ $\"\"$ .

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$\"\"$

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The distance travel during the first $\"\"$ seconds $\"\"$ $\"\"$ .