To find the position of the particle when it is farthest to the right, we need to find the time at which the velocity is equal to zero and plug it into the position function.
The position of a particle at time t is given by the position function r(t). In order to find the position of the particle when it is farthest to the right, we need to find the time at which the particle reaches its maximum x-coordinate.
Since the velocity function v(t) is given, we can find this time by looking for when the velocity is equal to zero. Once we find this time, we can plug it back into the position function to find the x-coordinate of the particle at that time.