An object falling freely
Suppose an object falling vertically from rest takes 4 seconds to reach the ground. Here is how its velocity changes on the way down.
Second by second
velocity as the fall begins = 0
after 1 second = 9.8 m s−1
after 2 seconds = 19.6 m s−1
after 3 seconds = 29.4 m s−1
after 4 seconds, as it hits the ground = 39.2 m s−1
Each step adds another 9.8 — which is precisely what g means.
The graph
| t (s) | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| v (m s⁻¹) | 0 | 9.8 | 19.6 | 29.4 | 39.2 |
The velocity increases uniformly, so the graph is a straight line. The shaded region is the height the object fell.
Calculating the height
Method 1 — by formula
average velocity = (0 + 39.2) ÷ 2 = 19.6 m s−1
displacement = average velocity × time
= 19.6 m s−1 × 4 s = 78.4 m
Method 2 — from the graph
The area of the triangle under the line:
(39.2 × 4) ÷ 2 = 78.4 m
The same answer. The graph is not new physics — it is the same calculation seen as geometry.
Extra knowledge — air resistance
The calculation above ignores air resistance. That is why, in the real world, a feather and a stone do not fall at the same rate. For a dense object such as a stone or a fruit, though, this calculation gives a good approximation.