If R(t) Is the Position Vector of a Particle in the Plane

question 67

Multiple Choice

If r(t) is the position vector of a particle in the plane at time t, find the indicated vector.
-Find the velocity vector.
$\mathbf { r } ( \mathrm { t } ) = \left( - 8 \mathrm { t } ^ { 2 } - 3 \right) \mathbf { i } + \left( \frac { 1 } { 9 } \mathrm { t } ^ { 3 } \right) \mathbf { j }$

• A) \(v = ( - 16 ) i + \left( \frac { 2 } { 3 } t \right) j\)
• B) \(\mathbf { v } = ( - 16 \mathrm { t } ) \mathbf { i } + \left( \frac { 1 } { 3 } \mathrm { t } ^ { 2 } \right) j\)
• C) \(\mathbf { v } = ( - 16 \mathrm { t } ) \mathbf { i } - \left( \frac { 1 } { 3 } \mathrm { t } ^ { 2 } \right) \mathbf { j }\)
• D) \(\mathbf { v } = \left( \frac { 1 } { 3 } \mathrm { t } ^ { 2 } \right) \mathbf { i } + ( - 16 \mathrm { t } ) \mathbf { j }\)

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Definitions:

Error-Prone

Error-prone describes a situation or system that is likely to make mistakes or contain errors.

Relatively Accurate

Describes information or measurements that are generally correct or precise when compared to a standard or expected value.

Eyewitness Events

Incidents or occurrences directly observed by an individual, often discussed in the context of legal justice to assess their reliability and accuracy.

Eyewitness Memory

The recall by individuals of events they have witnessed, significant in legal contexts but known for its potential for inaccuracy and susceptibility to suggestion.