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**shilz222** A tire rolls in a straight line without slipping. Its center moves with constant speed $\displaystyle V $. A small pebble lodged in the read of the tire touches the road at $\displaystyle t = 0 $. Find the pebble's position, velocity, and acceleration as functions of time.

So $\displaystyle \bold{v} = \dot{r} \bold{\hat{r}} + r \theta \bold{\hat{\theta}} $.

Would it just be $\displaystyle \bold{v} = V \bold{\hat{r}} + Vt \omega \bold{\hat{\theta}} $ and $\displaystyle \bold{a} = -Vt \omega^{2} \bold{\hat{r}} + 2V \omega \bold{\hat{\theta}} $?

Then to find the position as a function of time, integrate the velocity? Actually, should I use Cartesian coordinates instead of polar coordinates?

Thanks