A particle moves along a line with velocity given by v(t)=t2−6t+5 meters per second for 0≤t≤7 seconds.
(a) Determine all values of t in the interval 0≤t≤7 at which the particle changes direction.
(b) Using a calculator, evaluate the particle’s displacement on the interval 0≤t≤7, correct to three decimal places.
(c) Using appropriate computation, determine the total distance traveled by the particle on the same interval, correct to three decimal places.
(d) Compare the numerical answers from parts (b) and (c). Explain what their signs and relative sizes reveal about the particle’s motion.