$\"\"$

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The velocity of a particle is $\"\"$ , $\"\"$ .

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Find acceleration function.

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$\"\"$

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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The rate of change in velocity is acceleration: $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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The acceleration function is $\"\"$ .

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$\"\"$

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Find position function.

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$\"\"$ .

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Apply integral on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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The position function is $\"\"$ .

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At time $\"\"$ , $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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The position function is $\"\"$ .

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$\"\"$

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The acceleration function is $\"\"$ .

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The position function is $\"\"$ .