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

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) $s ( t ) = \frac { \left( t ^ { 2 } + 6 \right) ^ { 5 } } { 10 } + \frac { 3 t } { 2 } + C$