A particle moves along a straight line for 0≤t≤12 seconds. The velocity–time graph of the motion is described verbally as follows.
• From t=0 to t=4 s, v(t) increases linearly from −6 m/s to 2 m/s.
• From t=4 to t=7 s, v(t) remains constant at 2 m/s.
• From t=7 to t=12 s, v(t) decreases linearly to −4 m/s at t=12 s.
Assume v(t) is continuous everywhere except for its change in slope at t=4 s and t=7 s.
(a) Describe the intervals on which the particle is moving to the right and the intervals on which it is moving to the left. Explain your reasoning in terms of the given velocity data.
(b) On which time interval is the speed of the particle increasing? On which interval is the speed decreasing? Justify your answers without explicitly computing acceleration.
(c) At what times in 0≤t≤12 is the acceleration of the particle equal to zero? Explain how you know from the description of the velocity graph.
(d) Compare the magnitude of the particle’s velocity at t=2 s with that at t=10 s. Which is greater, and by how much? Provide a brief justification.