Question

A particle's motion is represented by the position equation s(t) = t² -t, t ≥ 0, where s is measured in feet and is measured in seconds. The particle moves to the right when (A) t > 0 (B) t > 1 (C) t > 1/2 (D) t > 2

Answer 1

The particle moves to the right for t > 1/2 seconds, as determined by solving the inequality 2t - 1 > 0, which indicates when its velocity is positive.

Step-by-step explanation:

The question deals with the motion of a particle described by the position function s(t) = t² - t, where s is in feet and t is in seconds. To determine when the particle moves to the right, we should find when its velocity, which is the first derivative of the position function, is positive.

First, we calculate the velocity: v(t) = s'(t) = 2t - 1. For the particle to move to the right, its velocity must be greater than zero. Hence, we solve the inequality 2t - 1 > 0, which gives us t > 1/2.

Therefore, the correct answer is (C) t > 1/2, indicating that the particle moves to the right when t is greater than one-half of a second.