A velocity–time graph for a particle moving along a straight track is composed of line segments and constant sections described below (units are seconds for t and meters per second for v):
• v(0)=0 and increases linearly to v(3)=6,
• remains constant at 6 on 3<t≤7,
• decreases linearly to v(10)=0,
• decreases linearly further to v(13)=−4,
• remains constant at −4 on 13<t≤16.
Assume straight-line changes between the stated points. Let s(t) denote the particle’s position with s(0)=5 meters.
(a) Calculate the particle’s displacement on 0≤t≤16.
(b) Calculate the total distance the particle travels on 0≤t≤16.
(c) Determine s(16), the particle’s position at t=16 seconds.
(d) Compute the particle’s average velocity on 0≤t≤16 and interpret its sign.