Velocity — Speed with Direction

Velocity is a vector quantity that describes both the speed and direction of motion. It differs from speed, which only has magnitude. Average velocity is calculated as displacement divided by time. Objects moving in opposite directions have opposite signs of velocity.

Speed vs. Velocity

Property	Speed	Velocity
Type	Scalar (size only)	Vector (size and direction)
Definition	distance / time	displacement / time
Example	30 m/s	30 m/s northwards

A car going around a roundabout at a constant 20 m/s has constant speed but changing velocity because its direction keeps changing.

Calculating Velocity

$v = \frac{s}{t}$

Symbol	Quantity	Unit
$v$	velocity	m/s
$s$	displacement	m
$t$	time	s

Note

Displacement is distance measured in a specific direction. Walking 10 m east then 10 m back west gives a displacement of 0 m but a distance of 20 m.

Calculating Velocity

A car drives 240 m north in 12 s. What is its velocity?

$v = \frac{s}{t} = \frac{240}{12} = 20 \text{ m/s north}$

Positive and Negative Velocity

Since velocity has direction, we can assign positive and negative values:

If moving right = positive velocity, then moving left = negative velocity.

A ball thrown upward slows down (velocity decreases toward 0), then falls back (velocity becomes negative).

Uniform vs. Non-Uniform Velocity

Uniform velocity: same speed, same direction — straight line at constant speed.
Non-uniform velocity: speed or direction (or both) changes.

Real world: Car at a roundabout

A car enters a roundabout and drives at a steady 20 km/h all the way around. Its speed is constant at 20 km/h throughout, but its velocity changes every moment because the direction of travel continuously changes. This is why cornering forces (centripetal force) exist — a changing velocity means there must be an acceleration, even at constant speed.

Real world: Swimmer doing laps

A competitive swimmer completes a 50 m pool length in 25 s, then turns and swims back in 25 s. Taking the initial direction as positive:

Velocity for first length: $v = +\dfrac{50}{25} = +2 \text{ m/s}$
Velocity for return length: $v = -\dfrac{50}{25} = -2 \text{ m/s}$
Average velocity for the full 100 m round trip: $\dfrac{0}{50} = 0 \text{ m/s}$ (displacement = 0)

Real world: Wind affecting a cyclist

A cyclist rides at 8 m/s due east into a 3 m/s headwind. The wind has a velocity of −3 m/s (opposing motion). The cyclist's velocity relative to the ground is still +8 m/s, but they must apply more force to maintain it — direction matters in the real world.

Tip

Where do you see this in real life? Weather forecasts always give wind as a velocity ("30 km/h from the south-west") not just a speed. Air traffic controllers track aircraft velocities (speed + direction) to avoid collisions. Sports coaches analyse player velocity vectors to improve tactics.

Practice Problems

A swimmer crosses a 50 m pool in 40 seconds. What is their velocity?

Show answer

v = s/t = 50/40 = 1.25 m/s (in the direction of travel)

A car travels at a constant speed around a bend. Is its velocity constant?

Show answer

No. Even though the speed is constant, the direction is changing. Velocity is a vector, so changing direction means changing velocity.

A plane flies 600 km east in 1 hour, then 600 km back west in 1 hour. What is its average velocity for the whole journey?

Show answer

Total displacement = 0 (it returned to the start). Average velocity = 0/2 = 0 m/s. (But average speed = 1200/2 = 600 km/h.)