$\"\"$

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Initial speed of the bike $\"\"$ m/s.

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Accleration of the bike $\"\"$ .

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Vertical distance from top of the hill to the bottom $\"\"$ .

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$\"\"$

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Where $\"\"$ is distance travelled.

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$\"\"$ is time in sec.

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Substiute the values of $\"\"$ in the equation $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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The obtained equation is in the form of $\"\"$ .

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Where $\"\"$

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Use the quadratic equation to find the value of $\"\"$ .

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$\"\"$

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Substiute the values of $\"\"$ in the above equation.

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$\"\"$

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$\"\"$

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$\"\"$ or $\"\"$

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$\"\"$ or $\"\"$ .

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Since time is does not measured in negative values, $\"\"$ is not considered.

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Pattrick takes $\"\"$ sec to ride down the $\"\"$ m distance hill.

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$\"\"$

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Pattrick takes $\"\"$ sec to ride down the $\"\"$ m distance hill.