Question 4
An object starting from rest is subjected to a uniform acceleration and reaches a velocity of 12 m s-1 in 4 s. The velocity–time graph drawn for this motion is shown below.
| t (s) | 0 | 4 |
|---|---|---|
| v (m s⁻¹) | 0 | 12 |
What is the object's displacement over those 4 seconds?
The right answer is the one marked above.
24 m. The shaded region is a triangle, and its area equals the displacement:
displacement = ½ × 12 × 4 = 24 m
The average velocity route gives the same answer: (0 + 12) ÷ 2 = 6 m s-1, and multiplying by the time gives 6 × 4 = 24 m. In fact 12⁄2 is the average velocity — that is what the "halving" in the triangle formula amounts to.
48 m comes from forgetting to halve — but the object was not travelling at 12 m s-1 the whole time; it built up to it from 0.