AS Daily A Level Physics question
An object moves in a straight line. The displacement s from a fixed origin (in metres) is plotted against time t (in seconds). From t = 0 to 5.0 s, the graph is a straight line from s = +2.0 m at t = 0 to s = −3.0 m at t = 5.0 s. From t = 5.0 s to t = 15.0 s, the graph is horizontal at s = −3.0 m. Which statement must be true about the motion over 0 ≤ t ≤ 15.0 s, and about what happens if the rest interval (the horizontal part) is made much longer while the endpoints at t = 0 and when motion stops are unchanged?
Answer
The correct answer is D.
Correct: D — The average speed and the magnitude of the average velocity are both 0.33 m s−1, and they remain equal for any longer rest at −3.0 m; the ratio is 1 and stays 1. Over 0–15 s the distance travelled is 5.0 m and the displacement magnitude is also 5.0 m, so both averages are 5.0/15.0 ≈ 0.33 m s−1; extending the rest increases time but not distance or displacement, so both decrease proportionally and the ratio stays 1. A The sign of displacement does not reduce the magnitude of average velocity, and extending the rest does not make the ratio grow. B A stationary period does not make average speed exceed the magnitude of average velocity here; they are equal now and do not approach equality from above. C With longer rest both averages shrink at the same rate (same numerator, larger denominator), so the ratio does not become greater than 1. D Matches the calculation and the proportional reasoning: equality now and in the limiting case of very long rest.