A2 Daily A Level Physics question
In a lab, a trolley moves in a straight line along a track. Its displacement–time graph is a straight line with gradient +0.8 m s−1 from t = 0 to 5.0 s, then a straight line with gradient −0.4 m s−1 from t = 5.0 s to 10.0 s. Displacement is measured from the start point. What is the trolley’s displacement at t = 10.0 s?
Answer
The correct answer is B.
Correct: B — +2.0 m. The gradient of a displacement–time graph is velocity, so displacement over each interval is (0.8 m s−1 × 5.0 s) = +4.0 m and (−0.4 m s−1 × 5.0 s) = −2.0 m; total displacement = +4.0 + (−2.0) = +2.0 m. A +6.0 m — This adds distances (4.0 m + 2.0 m) and ignores direction; that is total distance, not displacement. B — Correct because it sums the signed displacements from each interval. C 0.0 m — Incorrectly assumes the forward and backward displacements cancel; they are +4.0 m and −2.0 m, which do not cancel to zero. D −2.0 m — Reverses the sign and magnitude as if the backward motion were larger than the forward motion, which it is not.