The Velocity of a Particle Moving in a Straight Line $v = e ^ { 3 t } + 3 t$

question 13

Multiple Choice

The velocity of a particle moving in a straight line is given by $v = e ^ { 3 t } + 3 t$ .
Find an expression for the position s after a time t.

• A) \(s ( t ) = 3 e ^ { 3 t } + 3 + C\)
• B) \(s ( t ) = \frac { 1 } { 3 } e ^ { 3 t } + \frac { 3 } { 2 } t ^ { 2 } + C\)
• C) \(s ( t ) = \frac { 1 } { 3 } e ^ { 3 t } + 6 t ^ { 3 } + C\)
• D) \(s ( t ) = \frac { 1 } { 3 } e ^ { 4 t } + \frac { 3 } { 2 } t ^ { 2 } + C\)
• E) \(s ( t ) = e ^ { 3 t } + 3 t ^ { 2 } + C\)

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Definitions:

Hierarchy Of Needs

A motivational theory in psychology comprising a five-tier model of human needs, from physiological to self-actualization, proposed by Abraham Maslow.

Maslow

Maslow refers to Abraham Maslow, a psychologist best known for formulating the hierarchy of needs, a theory of psychological health predicated on fulfilling innate human needs in priority, culminating in self-actualization.

Basic Needs

Fundamental requirements for human survival and well-being, such as food, water, shelter, and safety, which are essential for maintaining life.

Rogers

A psychologist known for developing the person-centered approach to therapy, emphasizing the human potential for growth, self-understanding, and psychological healing.