Theory question 114
DynamicsA body, moving at 20 ms−1 accelerates uniformly at 2½ ms−2 for 4 seconds. It continues the journey at this speed for 8 seconds, before coming to rest t seconds after with uniform retardation. If the ratio of the acceleration to retardation is 3 : 4, (a) sketch the velocity − time graph of the journey; (b) find t; (c) find the total distance of the journey.
Show the model answer
Model answer
Speed after 4 s: 20 + 2.5 × 4 = 30 ms⁻¹.
(a) Sketch: a line from (0, 20) up to (4, 30), horizontal to (12, 30), then down to (12 + t, 0); label axes.
(b) Retardation = (4/3) × 2.5 = 10/3 ms⁻², so t = 30 ÷ (10/3) = 9 s.
(c) Distance = area = ½(20 + 30)(4) + 30 × 8 + ½ × 30 × 9 = 100 + 240 + 135 = 475 m.
Explanation
Distance is the area under the velocity–time graph.