# Find the pebble's position, velocity, and acceleration

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

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

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

Then to find the position as a function of time, integrate the velocity?

Thanks

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## Answers and Replies

Avodyne
So use the transformations $$x = r \cos \theta$$, $$y = r \sin \theta$$?