A particle moves along a straight line with velocity v(t), measured in meters per second, described verbally below.
• On the interval 0≤t≤3 seconds, v(t) increases linearly from 0m/s to 6m/s.
• On the interval 3<t≤5 seconds, v(t) is constant at 6m/s.
• On the interval 5<t≤8 seconds, v(t) decreases linearly to −4m/s at t=8 seconds.
• On the interval 8<t≤10 seconds, v(t) increases linearly back to 0m/s at t=10 seconds.
Assume the positive direction of motion is away from the origin.
(a) Describe the intervals on 0≤t≤10 during which the particle is speeding up and the intervals during which it is slowing down. Justify your answer by referring to the signs of velocity and acceleration.
(b) Identify all times at which the particle changes direction. Explain how the graph indicates these times.
(c) Suppose the particle begins at a position to the right of the origin at t=0. Over which sub-intervals of 0≤t≤10 is the particle moving farther from the origin, and over which sub-intervals is it moving closer to the origin? Provide reasoning based on the given velocity information.