Let $x_1(t) = t + \cos(t)$ and $x_2(t) = t + \sin(t)$ describe the positions along the $x$-axis of two particles, for $0 ≤ t ≤ 3$. 10-113 HW eTool (Desmos).

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

   Step (a):

   $v_1=1-\sin(t)$

   $v_2=\sin(t)+t\cos(t)$

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).