A particle moves along a straight line so that its velocity (in meters per second) at time t seconds is given by
v(t)=6t2−4+3e−t.
At time t=0, the particle is 5 meters to the right of the origin.
(a) Determine the particle’s position function s(t) for t≥0. Express your answer in simplest form.
(b) Calculate the particle’s displacement (signed distance) during the first 2 seconds.
(c) Is the total distance traveled during the first 2 seconds equal to the displacement you found in part (b)? Explain your reasoning without additional calculation.