Question 3
An object falling vertically from rest reaches the ground in 4 s. The velocity–time graph for the motion is shown below.
| t (s) | 0 | 4 |
|---|---|---|
| v (m s⁻¹) | 0 | 39.2 |
From what height did it fall? (g = 9.8 m s-2)
The right answer is the one marked above.
78.4 m. At the moment it lands the velocity is 39.2 m s-1. The height fallen is the area of the triangle under the graph:
height = (0 + 39.2) ÷ 2 × 4 s = 19.6 × 4 = 78.4 m
That is average velocity × time. 39.2 m comes from using the value of the velocity as the height; 156.8 m comes from forgetting to halve.