$\"\"$

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

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(a)

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

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$\"\"$ .

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The particle is initially at rest $\"\"$ .

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

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$ .

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

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

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At the 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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(b) Find values of $\"\"$ for which the particle is at rest.

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The particle is at rest the velocity is zero.

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Equate $\"\"$ .

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$\"\"$

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

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The values of $\"\"$ for particle is at rest is $\"\"$ , where $\"\"$ .

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$\"\"$

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(a)

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The velocity function of the particle is $\"\"$ .

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The position function is $\"\"$ .

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(b) The values of $\"\"$ for the particle is at rest is $\"\"$ , where $\"\"$ .