A weather report might say the wind blows "at 20 km/h from the northwest." That is more than a speed; it also says which way. Speed together with direction is called velocity, and it is built from displacement the way speed is built from distance.
Key idea
Velocity is speed with a direction: how fast and which way. Average velocity = displacement ÷ time. On a line we show the direction with a sign: + one way, − the other.
Why it works
Two cars both going 50 km/h, one north and one south, are clearly not doing the same thing: in an hour they end up 100 km apart. Speed can't tell them apart, but velocity can: $+50$ km/h and $-50$ km/h. That is why changing direction changes your velocity even when the speedometer doesn't move.
Worked example: Speed and velocity on one trip
A runner jogs 300 m east, then 100 m west, in a total of 100 s. Find her average speed and her average velocity.
- Distance: $300 + 100 = 400$ m. Average speed: $400 \div 100 = 4$ m/s.
- Displacement (east positive): $300 - 100 = +200$ m.
- Average velocity: $+200\,\mathrm{m} \div 100\,\mathrm{s} = +2$ m/s, which means 2 m/s east.
Answer: Average speed 4 m/s; average velocity 2 m/s east
Worked example: Same speed, new velocity
A cyclist rides at 6 m/s east, turns around and rides at 6 m/s west. Take east as positive. How did her velocity change?
- Before: $v = +6$ m/s. After: $v = -6$ m/s.
- Change: $-6 - (+6) = -12$ m/s, even though her speed stayed 6 m/s.
Answer: From $+6$ m/s to $-6$ m/s
Common mistake
Thinking two cars going 50 km/h in opposite directions have the same velocity. They have the same speed; their velocities are $+50$ and $-50$ km/h. Check: if two velocities are equal, the objects move together and the gap between them never changes.
Earth carries you around the Sun at about 30 km/s. That speed hardly changes during the year, but the direction turns all the way around, so Earth's velocity is always changing.