Let $x_1 (t) = t +\operatorname{ cos} t$ and $x_2 (t) = t\operatorname{ sin} t$ describe the positions along the $x$-axis of two particles, for $0 ≤ t ≤ 3$.

1. At what time(s) in this interval do the particles have the same velocity?

2. What are the positions of the particles at these times?

   Hint (b):

   Evaluate the original (position) equations for the value of $t$ you obtained in part (a).