Find the pebble's position, velocity, and acceleration

[tronter]

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

 

[Avodyne]

You need to do this in cartesian coords, because the center keeps moving.

 

[tronter]

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

 

[Thyferra2680]

I had to do a problem similar to this, and I still don't understand it...