Space Find the Acceleration $\mathbf { a } ( t )$

question 20

Multiple Choice

$\text { The position vector } \mathbf { r } ( t ) = 4 t \mathbf { i } + 2 t \mathbf { j } + \frac { 1 } { 6 } t ^ { 2 } \mathbf { k } \text { describes the path of an object moving in }$ space. Find the acceleration $\mathbf { a } ( t )$ of the object.

• A) \(\mathbf { a } ( t ) = \frac { 1 } { 6 } \mathbf { k }\)
• B) \(\mathbf { a } ( t ) = 4 \mathbf { i } + 2 \mathbf { j }\)
• C)\(\mathbf { a } ( t ) = 4 \mathbf { i } + 2 \mathbf { j } + \frac { 1 } { 3 } \mathbf { k }\)
• D) \(\mathbf { a } ( t ) = 4 \mathbf { i } + 2 \mathbf { j } + 2 \mathbf { k }\)
• E) \(\mathbf { a } ( t ) = \frac { 1 } { 3 } \mathbf { k }\)

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Definitions:

Standard Costs

Predetermined costs for materials, labor, and overhead used as a benchmark to assess the performance of actual costs.

Direct Labor Time Variance

The difference between the estimated time to complete a job and the actual time taken, impacting manufacturing costs.

Standard Costs

Predetermined costs assigned to goods and services, used in setting a budget and analyzing performance.

Actual Costs

The actual expenses incurred in the production of goods or services, as opposed to estimated or standard costs.