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:

Place Theory

A hearing theory that suggests different areas of the cochlea are activated by different frequencies of sound, enabling us to distinguish pitches.

Basilar Membrane

A membrane in the cochlea of the inner ear that plays a key role in the sense of hearing by vibrating in response to sound and facilitating auditory processing.

Lower Frequency

Refers to sounds or waves that have a lower rate of vibration, and thus a deeper pitch or longer wavelength.

Higher Frequency

Refers to a greater number of cycles or events per unit time, often used in the context of waves or signals.