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For the position function: r(t) = t cos (t) i + t sin(t) j + t^2 k , t_0 = 0. Find the four...

Question:

For the position function: {eq}r(t) = t cos (t) i + t sin(t) j + t^2 k , t_0 = 0. {/eq} Find the four acceleration components {eq}T(t_0), a T(t_0), a N(t_0), \ and \ N(t_0) {/eq}

Finding the Acceleration Components:

The acceleration components of the tangential and normal vectors, then the unit tangent vector and the unit normal vectors are evaluated by using the velocity and acceleration vectors. The parameter value {eq}\displaystyle t {/eq} should be considered as {eq}\displaystyle t_0 {/eq}.

Answer and Explanation:

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We consider the given position function {eq}\displaystyle r(t) = t \cos (t) \vec{i} + t \sin(t) \vec{j} + t^2 \vec{k} , {/eq} at...

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