AS Daily A Level Physics question
A walker moves along a straight path. From t = 0 to 5 s, the displacement–time graph is a straight line with gradient +3.0 m s⁻¹. From 5 s to 10 s, the line has gradient −1.0 m s⁻¹. Over the 0–10 s interval, how does the average speed compare with the magnitude of the average velocity?
Answer
The correct answer is D.
Correct: D — Average speed is twice the magnitude of average velocity. Over 10 s the walker goes +15 m then −5 m, so total distance = 20 m and displacement = +10 m; average speed = 20/10 = 2.0 m s⁻¹ and |average velocity| = 10/10 = 1.0 m s⁻¹, giving a factor of 2. A They would be equal only if there were no change in direction so distance equalled displacement; here turning back makes distance larger. B Turning back increases the distance travelled, so average speed is larger, not smaller, than the magnitude of average velocity. C 1.5 is an incorrect ratio (e.g. from a mistaken averaging of gradients); the correct ratio is 2 from 20/10 divided by 10/10. D This matches the calculated 2:1 ratio from the distances and displacement.