A particle moves on a straight line v(t)=sinwt cos ^{3} wt. find the position s(t) if s(0)=0.

I've done this style of question before, but the two variables throw me off.

I assume that u=cos(wt) but am unsure.

Question

A particle moves on a straight line v(t)=sinwt cos ^{3} wt. find the position s(t) if s(0)=0.

I've done this style of question before, but the two variables throw me off. 

I assume that u=cos(wt) but am unsure.

anonymous · Answer

then du=-sin(wt)

anonymous · Answer

-du=sin(wt)

anonymous · Answer

$$- \int\limits_{?}^{?} (u)^{3} du$$

anonymous · Answer

$$-\frac{ 1 }{ 4 } (u)^{4} +c$$

anonymous · Answer

$$- \frac{ (coswt)^{4} }{ 4 } +c$$

then insert s(0)=0 so.....

$$- \frac{ (cosw(0))^{4} }{ 4 } +c$$=0

... but w is still an unknown...

anonymous · Answer

woooooooo no idea whats going on....

anonymous · Answer

unless -cosw(0)=0...

then c=0...
yeah i'm confused, doesn't seem right.

sirm3d · Answer

$$\mathrm du=-w\cdot\sin wt\,\mathrm dt$$