A particle moves along a straight line so that its velocity (in meters per second) at time t seconds is given by
v(t)=4t3−6t+1,0≤t≤3.
At time t=1 the particle is 5 meters to the right of the origin.
(a) Determine the particle’s position function s(t) for 0≤t≤3. Express your answer in simplest form and include appropriate units.
(b) Calculate the particle’s displacement (signed change in position) during the interval 0≤t≤3.
(c) Compute the total distance traveled by the particle on the interval 0≤t≤3. Clearly justify any intervals on which you change the sign of the integrand in your calculations.