A particle moves along a horizontal line so that its velocity (in meters per second) at time t seconds is given by v(t)=3t2−12t+5 for 0≤t≤4.
(a) Calculate the displacement of the particle during the time interval 0≤t≤4 seconds.
(b) Determine the particle’s average velocity over the same interval and state its units.
(c) At what time in 0≤t≤4 is the particle at rest? Use this information along with your answers to parts (a) and (b) to decide whether the particle ever reverses direction on the interval.
(d) Interpret the sign of the average velocity you found in part (b) in terms of the particle’s overall motion.
(a) Calculate the displacement ∫04v(t)dt.
(b) Determine the average velocity on [0,4].
(c) Find any time(s) when v(t)=0 in [0,4] and use them to discuss reversal of direction.
(d) Interpret the sign of the average velocity.