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:

Experimental Group

In research, the group of subjects who are exposed to the variable under investigation, in contrast to the control group.

Independent Variable

In experimental research, the variable that is intentionally manipulated by the researcher to explore its effect on a dependent variable.

Manipulation

The skillful or devious exertion of influence over someone for personal gain or to serve one's purposes.

Experimental Technique

It is a method or procedure used in scientific research to test hypotheses by systematically varying parameters and observing the outcomes.