$\"\"$

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A particle is moving with a acceleration $\"\"$ , $\"\"$ and $\"\"$ .

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The acceleration of the object is $\"\"$ , where $\"\"$ is the velocity.

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Hence $\"\"$ .

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The anti derivative of $\"\"$ is $\"\"$ .

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The anti derivative of $\"\"$ is $\"\"$ .

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The antiderivative of $\"\"$ is

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$\"\"$

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$\"\"$ , where $\"\"$ is the constant.

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The velocity of the object is $\"\"$ , where $\"\"$ is the distance.

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Hence $\"\"$ .

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The antiderivative of $\"\"$ is

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$\"\"$

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$\"\"$ , where $\"\"$ is the constant.

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$\"\"$

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The distance of the object is $\"\"$ .

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Here $\"\"$ .

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

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$\"\"$

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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Therefore the position of the particle is $\"\"$ .

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$\"\"$

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The position of the particle is $\"\"$ .