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**1. Homework Statement**

A particle starts at (d, 0) in polar coordinates and has a velocity of

[tex]\vec{v}=(u \sin{\theta} - v)\hat{r} + u \cos{\theta} \hat{\theta} [/tex]

where v > u

Find the position vector of the particle as a function of time.

**2. Homework Equations**

[tex]\vec{v}=\frac{d\vec{r}}{dt}[/tex]

**3. The Attempt at a Solution**

I'm not sure how to integrate the expression for v to get the position of a particle. Since the unit vectors are changing, I can't just integrate the components individually like in Cartesian coordinates right?

I also read that [tex]\dot{\textbf{r}}=\dot{r}\hat{\textbf{r}}+ r\dot{\theta}\hat{\textbf{\theta}}[/tex]

But I'm not sure if this helps me.

Thanks in advance for the help :)

P.S. How do I bold the letters? I used \textbf but it doesn't seem to have an effect.