The Velocity of a Particle Moving in a Straight Line $v = t \left( t ^ { 2 } + 6 \right) ^ { 4 } + 3 t$

question 61

Multiple Choice

The velocity of a particle moving in a straight line is given by $v = t \left( t ^ { 2 } + 6 \right) ^ { 4 } + 3 t$ .
Find an expression for the position s after time t.

• A) \(s ( t ) = \frac { \left( t ^ { 2 } + 6 \right) ^ { 5 } } { 10 } + 3 t ^ { 2 } + C\)
• B) \(s ( t ) = \frac { \left( t ^ { 2 } + 6 \right) ^ { 5 } } { 5 } + \frac { 3 t ^ { 2 } } { 2 } + C\)
• C) \(s ( t ) = \frac { \left( t ^ { 2 } + 6 \right) ^ { 5 } } { 10 } + \frac { 3 t ^ { 2 } } { 2 } + C\)
• D) \(s ( t ) = \frac { t \left( t ^ { 2 } + 6 \right) ^ { 5 } } { 10 } + \frac { 3 t ^ { 2 } } { 2 } + C\)
• E) \(s ( t ) = \frac { \left( t ^ { 2 } + 6 \right) ^ { 5 } } { 10 } + \frac { 3 t } { 2 } + C\)

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Definitions:

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A category of vegetables with green leaves, rich in vitamins, minerals, and fiber, including spinach, kale, and lettuce; vital for a healthy diet.

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A fat-soluble vitamin important for vision, the immune system, and skin health.

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Biological molecules that catalyze the breakdown of complex food particles into simpler substances for absorption and assimilation by the body.