Introduction

Suppose two cars are travelling at 60 km/h. One is driving north, while the other is driving south. Although their speeds are the same, their motions are clearly different because they are travelling in different directions.

To fully describe motion, physicists use velocity instead of speed. Velocity tells us both how fast an object is moving and the direction in which it is moving. This makes velocity one of the most important quantities in mechanics and prepares us for studying acceleration, forces, and more advanced motion.

What is Velocity?

Velocity is speed in a specified direction.

More precisely, velocity is the rate of change of displacement with time.

Unlike speed, velocity tells us:

• How fast an object is moving.
• The direction in which it is moving.

Because it includes direction, velocity is a vector quantity.

Examples:

• 15 m/s east
• 80 km/h north
• 5 m/s downward

A value such as 20 m/s alone describes speed, not velocity.

Speed vs Velocity

Speed and velocity are closely related, but they are not the same.

Remember:

• Speed uses distance.
• Velocity uses displacement.

Calculating Average Velocity

Average velocity is calculated using displacement rather than distance.

The equation is:

\( Average \ Velocity = \frac{Displacement}{Time} \)

​

Notice that this is different from the equation for average speed, which uses distance.

SI Units of Velocity

The SI unit of velocity is:

metres per second (m/s)

Other common units include:

• kilometres per hour (km/h)
• centimetres per second (cm/s)

Since velocity includes direction, the unit should always be accompanied by a direction whenever possible.

Examples:

• 12 m/s east
• 5.5 m/s upward
• 80 km/h north

Example 1: Straight-Line Motion

A cyclist rides 120 m east in 20 s.

Step 1

Write the known values.

Displacement = 120 m east

Time = 20 s

Step 2

Use the equation.

\( Average \ Velocity = \frac{120}{20} \)​

Step 3

Calculate.

Average Velocity = 6.0 m/s east

Answer: The cyclist's average velocity is 6.0 m/s east.

Example 2: Returning Toward the Starting Point

A student walks:

• 50 m east
• Then 20 m west

Time taken = 35 s

Distance

50 + 20 = 70 m

Displacement

50 − 20 = 30 m east

Average Velocity

\( \frac{30}{35} \) = 0.86 m/s east

Although the student travelled 70 m, the average velocity depends only on the 30 m displacement.

Average Speed vs Average Velocity

These quantities are often confused.

For a journey involving changes in direction:

• Average speed is usually greater than the magnitude of the average velocity.

Positive and Negative Velocity

In one-dimensional motion, direction is often represented using positive and negative signs.

For example:

• East = Positive (+)
• West = Negative (−)

or

• North = Positive (+)
• South = Negative (−)

The choice is arbitrary, but it must remain consistent throughout the problem.

Example:

• +8 m/s means 8 m/s east.
• −8 m/s means 8 m/s west.

The negative sign indicates direction, not that the object is slowing down.

Interpreting Positive and Negative Velocities

Consider a car travelling along a straight road.

The sign tells us the direction of motion, while the magnitude tells us how fast the object is moving.

When are Speed and Velocity Equal?

The numerical values of speed and the magnitude of velocity are equal only when:

• The object moves in a straight line.
• The object never changes direction.

If an object changes direction:

• Distance becomes greater than displacement.
• Average speed becomes greater than the magnitude of average velocity.

Everyday Examples of Velocity

Velocity is important whenever direction matters.

Examples include:

• A pilot flying northwest.
• A ship sailing south.
• Wind blowing eastward.
• A football kicked toward the goal.
• A satellite orbiting Earth.

In each case, both speed and direction are needed to fully describe the motion.

Why Understanding Velocity is Important

Velocity is one of the fundamental quantities in mechanics.

It is used to:

• Calculate acceleration.
• Predict future positions.
• Analyse collisions.
• Study projectile motion.
• Design transport systems.
• Navigate aircraft and spacecraft.

Many later topics in physics rely on understanding velocity.

Real-World Connections

Velocity plays a crucial role in science and engineering.

Examples include:

• Pilots use velocity to navigate aircraft accurately.
• Meteorologists measure wind velocity to forecast weather.
• Engineers analyse the velocity of vehicles during crash testing.
• Astronomers measure the velocities of stars and galaxies to study the expansion of the Universe.
• GPS systems continuously calculate a vehicle's velocity to provide navigation and estimated arrival times.

Worked Example

A runner travels:

• 200 m north

in

• 25 s

Question

Calculate the runner's average velocity.

Solution

Step 1

Write the known values.

Displacement = 200 m north

Time = 25 s

Step 2

Use the equation.

\( Average \ Velocity = \frac{200}{25} \)​

Step 3

Calculate.

Average Velocity = 8.0 m/s north

Answer: The runner's average velocity is 8.0 m/s north.

Did You Know?

• Although Earth's surface rotates at speeds of up to 1,670 km/h near the equator, your velocity is constantly changing because your direction changes as Earth rotates.
• Astronomers use the Doppler effect to measure the velocities of distant stars and galaxies by observing changes in the wavelengths of light they emit.
• A racing car may have a very high speed, but when it travels around a circular track, its velocity is constantly changing because its direction is continually changing.

Key Terms

Velocity — The rate of change of displacement with time; speed in a specified direction.

Average Velocity — The total displacement divided by the total time taken.

Speed — The rate at which distance is travelled.

Displacement — The straight-line change in position from the starting point to the ending point.

Vector Quantity — A quantity that has both magnitude and direction.

Scalar Quantity — A quantity that has magnitude only.

Key Takeaways

• Velocity describes how fast an object moves and in what direction.
• Velocity is calculated using displacement, while speed is calculated using distance.
• Velocity is a vector quantity, meaning it has both magnitude and direction.
• Positive and negative velocities indicate opposite directions of motion, not faster or slower movement.
• Average velocity is found by dividing displacement by time.
• Understanding velocity provides the foundation for studying acceleration, projectile motion, and many other areas of mechanics.