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Step 1 :

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If $\"\"$ is the position vector of for a smooth curve C, then the tangential and normal components of acceleration are as follows.

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$\"\"$ and $\"\"$ .

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The unit tangent vector is $\"\"$ .

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Step 2 :

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The acceleration is $\"\"$

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The position vector is $\"\"$ and time $\"\"$ .

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Apply derivative on each side with respect to t.

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$\"\"$

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Substitute $\"\"$ in above equation.

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$\"\"$

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Find the tangent vector $\"\"$ :

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$\"\"$

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Substitute corresponding values in above equation.

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$\"\"$

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Step 3 :

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Differentiate $\"\"$ with respect to t.

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$\"\"$

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Substitute $\"\"$ in above equation.

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$\"\"$

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Find the tangential component of acceleration $\"\"$ : $\"\"$

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Substitute corresponding values in above equation.

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$\"\"$

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Step 4 :

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The normal component of acceleration is $\"\"$ :

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$\"\"$

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Substitute corresponding values in above equation.

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$\"\"$

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Find $\"\"$ :

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The acceleration is $\"\"$

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$\"\"$

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Substitute corresponding values in above equation.

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$\"\"$

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Solution :

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$