Find the Acceleration of a Particle with the Following Position $$\mathbf { r } ( t ) = \left\langle 2 t ^ { 2 } - 2,4 t \right\}$$

question 115

Multiple Choice

Find the acceleration of a particle with the following position function.
$$\mathbf { r } ( t ) = \left\langle 2 t ^ { 2 } - 2,4 t \right\}$$
Select the correct answer.

• A) \(\mathbf { a } ( t ) = 4 \mathbf { i }\)
• B) \(\mathbf { a } ( t ) = 2 t \mathbf { i } + 2 \mathbf { j }\)
• C) \(\mathbf { a } ( t ) = ( 2 + 4 t ) \mathbf { i } - 2 \mathbf { j }\)
• D) \(\mathbf { a } ( t ) = 2 \mathbf { i } - \mathbf { j }\)
• E) \(\mathbf { a } ( t ) = 4 t \mathbf { i } + 2 \mathbf { j }\)

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Definitions:

Agitated

A state of nervousness or unrest, often displayed by continuous movement or emotional upset.

Quiet Time

Scheduled periods in healthcare or daily settings designed to provide a calm atmosphere conducive to rest, recovery, or focused activities.

Proprioception

The sense of the relative position of one's own parts of the body and strength of effort being employed in movement.

Ambulating

The act of walking or moving from one place to another; especially referred to in medical contexts related to patients.