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

Multiple Choice

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

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