A Particle Moves on a Straight Line with Velocity Function $v ( t ) = \sin a t \cos ^ { 3 } a t$

Multiple Choice

A particle moves on a straight line with velocity function $v ( t ) = \sin a t \cos ^ { 3 } a t$ . Find its position function $s = f ( t )$ if $f ( 0 ) = 0$ .

A) $\frac { \cos ^ { 5 } \omega t + 1 } { 5 a }$
B) $\frac { \sin ^ { 2 } a t + 1 } { 7 a }$
C) $\frac { \sin ^ { 3 } a t - 1 } { 3 a }$
D) $\frac { 1 - \cos ^ { 4 } \omega t } { 4 a }$
E) $\frac { 1 - \cos ^ { 6 } \omega t + 1 } { 6 \omega }$