The Acceleration Function (In M $s ^ { 2 }$

Multiple Choice

The acceleration function (in m / $s ^ { 2 }$ ) and the initial velocity are given for a particle moving along a line. Find the velocity at time t and the distance traveled during the given time interval. $a ( t ) = t + 4 , v ( 0 ) = 3,0 \leq t \leq 10$

A) $v ( t ) = \frac { t ^ { 2 } } { 2 } + 3 t \mathrm {~m} / \mathrm { s } , 571 \frac { 2 } { 3 } \mathrm {~m}$
B) $v ( t ) = \frac { t ^ { 2 } } { 2 } + 3 \mathrm {~m} / \mathrm { s } , 596 \frac { 2 } { 3 } \mathrm {~m}$
C) $v ( t ) = \frac { t ^ { 2 } } { 2 } + 4 t + 3 \mathrm {~m} / \mathrm { s } , 496 \frac { 2 } { 3 } \mathrm {~m}$
D) $v ( t ) = \frac { t ^ { 2 } } { 2 } + 3 t \mathrm {~m} / \mathrm { s } , 546 \frac { 2 } { 3 } \mathrm {~m}$
E) $v ( t ) = \frac { t ^ { 2 } } { 2 } + 4 t + 3 \mathrm {~m} / \mathrm { s } , 396 \frac { 2 } { 3 } \mathrm {~m}$