Hey all i was doing this mechanics 1 question but two parts of it dont make sense to me so i was wondering if i was doing the question correct.

**Find velocity of the particle, $\displaystyle \dot{x}(t) $ for $\displaystyle t > 0 $** $\displaystyle \ddot{x} = \sin t. $ Integrating this gives $\displaystyle \dot{x} = - \cos t + c $ Now thats the bit that tricks me, its says for t > 0. But we are not given any conditions for t > 0. So do i just plug in where $\displaystyle t = 0, \dot{x}=0 $

hence $\displaystyle c = 0?$

$\displaystyle

\therefore \dot{x} = - \cos t$

**The same problem when finding the position of the particle for t>0.**
Do i just integrate $\displaystyle \dot{x}$ and sub in where t=0, x=0 ?

**Finally, i dont have a clue on how to draw the distance or the velocity.**
Hopefully you lot can help me out,

.

Thanks.