$\"\"$

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The velocity function is $\"\"$ , $\"\"$ .

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(a)

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Find the displacement.

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The velocity is defined as change in displacement over a change in time.

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$\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Displacement of the particle is $\"\"$ ft.

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$\"\"$

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Find the total distance.

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$\"\"$ , $\"\"$ .

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The total distance $\"\"$ .

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$\"\"$ is positive when $\"\"$ .

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Solve $\"\"$

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Solution of $\"\"$ is $\"\"$ , $\"\"$ .

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$\"\"$ is negative when $\"\"$ .

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Solve $\"\"$ .

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Solution of $\"\"$ is $\"\"$ .

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The limits of the integral is $\"\"$ .

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$\"\"$ is negative over the interval $\"\"$ .

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$\"\"$ is positive over the interval $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The total distance $\"\"$ ft.

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The total distance $\"\"$ ft.

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$\"\"$

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(a) Displacement of the particle is $\"\"$ ft.

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(b) The total distance $\"\"$ ft.