A particle moves along a straight line for 0≤t≤10 seconds. Its velocity v(t) and acceleration a(t) are continuous on this interval. The signs (positive or negative) of v(t) and a(t) on selected sub-intervals are summarized below.
```
Time interval (s) 0<t<2 2<t<4 4<t<6 6<t<8 8<t<10
----------------------------------------------------------------
Sign of v(t) + + – – +
Sign of a(t) + – – + +
```
Answer the following questions about the motion of the particle. Give clear verbal explanations that cite appropriate features of the table in your reasoning.
(a) For each sub-interval shown in the table, indicate whether the particle is moving to the right or to the left. Justify your answer.
(b) Determine on which sub-intervals the particle’s speed is increasing and on which sub-intervals the speed is decreasing. Explain your reasoning.
(c) Describe what happens to the particle’s speed at t=2 s and t=6 s. State whether each of these times corresponds to a local maximum, a local minimum, or neither for the speed, and justify your conclusions.