A car's velocity as a function of time is represented by the following description of…
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A car's velocity as a function of time is represented by the following description of a velocity–time graph for the interval 0 ≤ t ≤ 7 s. From t = 0 s to t = 2 s, the graph is a straight line that increases uniformly from v = 0 m/s to v = 10 m/s. From t = 2 s to t = 5 s, the velocity increases from 10 m/s to 25 m/s along a curve that becomes steeper with time. From t = 5 s to t = 7 s, the graph is a straight line that decreases uniformly from 25 m/s to 15 m/s. Three points are labeled on the graph: point P at t = 1 s, point Q at t = 3.5 s, and point R at t = 6 s.
(a) Rank the instantaneous accelerations at points P, Q, and R from most positive to least. Explain carefully.
(b) During which one-second interval is the car’s displacement the greatest? Choose from 0–1 s, 1–2 s, 2–3 s, 3–4 s, 4–5 s, 5–6 s, or 6–7 s, and justify using the graph.
(c) Sketch a possible acceleration–time graph for the interval 0 ≤ t ≤ 7 s that is consistent with the described velocity–time graph. On your sketch label approximate values at t = 1 s, 3.5 s, and 6 s.
(d) Determine the car’s average acceleration over the entire 7-s interval and explain how your answer is related to features of the velocity–time graph.