The Vector R(t) Is the Position Vector of a Particle

question 34

Multiple Choice

The vector r(t) is the position vector of a particle at time t. Find the angle between the velocity and the acceleration vectors at time t = 0.
- $$\mathbf { r } ( \mathrm { t } ) = \sin ^ { - 1 } ( 7 \mathrm { t } ) \mathbf { i } + \ln \left( 8 \mathrm { t } ^ { 2 } + 1 \right) \mathbf { j } + \sqrt { 7 \mathrm { t } ^ { 2 } + 1 } \mathbf { k }$$

• A) \(\frac { \pi } { 4 }\)
• B) \(\frac { \pi } { 3 }\)
• C) \(\frac { \pi } { 2 }\)
• D) 0

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Definitions:

Chromosome Number

The total count of chromosomes present in the nucleus of a cell, specific to each species.

Diploid

An organism or cell having two complete sets of chromosomes, typically one set from each parent.

Prophase I

The first stage of meiosis I where chromosomes condense, pair up, and exchange genetic material through crossing over, essential for genetic diversity.

Homologous Chromosomes

Pairs of chromosomes in a diploid organism that are similar in size, shape, and gene content, one inherited from each parent.