The Position Vector of a Particle Is R(t) $t = 0$

question 122

Multiple Choice

The position vector of a particle is r(t) . Find the requested vector.
-The acceleration at $t = 0$ for $r ( t ) = t ^ { 2 } i + \left( 8 t ^ { 3 } - 10 \right) j + \sqrt { 4 - 3 t } k$

• A) \(\mathbf { a } ( 0 ) = 2 \mathbf { i } - \frac { 3 } { 32 } \mathbf { k }\)
• B) \(\mathbf { a } ( 0 ) = 2 \mathbf { i } + \frac { 9 } { 32 } \mathbf { k }\)
• C) \(\mathbf { a } ( 0 ) = 2 \mathbf { i } - \frac { 9 } { 8 } \mathbf { k }\)
• D) \(\mathbf { a } ( 0 ) = 2 \mathbf { i } - \frac { 9 } { 32 } \mathbf { k }\)

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Definitions:

Proximate Cause

A principle in the law of negligence that determines whether the harm or injury suffered by the plaintiff was a foreseeable consequence of the defendant's action or inaction.

Legal Cause

The reason or motive for some action under law, often referring to the grounds for litigation or the principle reasons behind legal action.

Punitive Damages

Punitive damages are compensation awarded in addition to actual damages, intended to punish the defendant for egregious wrongdoing and deter similar future actions.

Negligence

A failure to exercise appropriate and/or ethical ruled care expected to be exercised amongst specified circumstances, leading to harm or damage.