AS Daily A Level Physics question
A motion sensor on a skateboarder records a straight run: starting from rest, the speed increases uniformly to 8.0 m/s in 4.0 s, remains at 8.0 m/s for the next 10.0 s, then decreases uniformly to rest over the final 2.0 s. Which statement must be true about the mean speed over the whole 16.0 s compared with the top speed?
Answer
The correct answer is D.
Correct: D — About 0.81 times the top speed. The distance is the area under the velocity–time graph: 0.5×4×8 = 16 m (speed-up) + 10×8 = 80 m (cruise) + 0.5×2×8 = 8 m (slow-down), total 104 m in 16 s, so mean speed = 104/16 = 6.5 m/s; ratio to 8.0 m/s is 6.5/8.0 ≈ 0.81. A is wrong because 0.50 comes from naïvely averaging 0 and 8 m/s without weighting by time. B is wrong because ≈0.65 arises if you count only the 10 s cruising distance (80 m) and ignore the triangular sections (giving 80/16 = 5.0 m/s → 0.625). C is wrong because the mean could equal the top speed only if the speed were 8.0 m/s for the entire 16 s, which it is not.