Average velocity
The table below gives the displacement measured at each second for another object travelling along a straight path.
| Time t (s) | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Displacement s (m) | 0 | 4 | 7 | 9 | 12 |
The displacement grows by 4 m, then 3 m, then 2 m, then 3 m. The change is not the same in every second, so the velocity is not uniform. In cases like this we can calculate an average velocity.
average velocity = 12 m ÷ 4 s = 3 m s−1
That says a uniform velocity of 3 m s−1 would have produced the same displacement in 4 s. In reality the object moved at different velocities at different moments.
Example — a bicycle journey
The table shows how the displacement of a child cycling along a straight road varied second by second.
| t (s) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| s (m) | 0 | 2 | 4 | 6 | 8 | 8 | 8 | 8 | 8 | 4 | 0 |
The journey has three parts
0 – 4 s: the displacement grows by 2 m every second — the child moves forward at a uniform velocity.
average velocity = (8 − 0) m ÷ 4 s = 2 m s−1
4 – 8 s: the displacement stays at 8 m. The child has not moved.
8 – 10 s: the displacement decreases. The motion is in the opposite direction, and by 10 s the child is back at the starting point.
velocity in the last 2 s = (0 − 8) m ÷ 2 s = −4 m s−1
How to read the minus sign
−4 m s−1 does not mean "the velocity is small". It means a velocity of 4 m s−1 in the backward direction. The sign of a vector states the direction, not the magnitude.