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:

Population Mean

The average of all the values in a population, serving as a measure of central tendency.

Sample Mean

The average value calculated from a sample of data points, used as an estimate of the population mean.

Sample Median

The middle value of a sample data set arranged in ascending or descending order, used as a measure of central tendency.

Bootstrapping

A statistical method that resamples a single dataset to create many simulated samples, used in assessing the precision of sample estimates.