The Velocity Formula, Explained with Examples

Velocity tells you how fast something is moving and in which direction. That direction part is what separates velocity from plain speed, and it is the single idea that trips most people up. In this guide you will see the core formula, the constant acceleration version, the difference between velocity and speed, and several worked examples you can follow step by step.

What is velocity?

Velocity is the rate at which an object changes its position. Because position changes have both a size and a direction, velocity is a vector quantity. A car driving 60 km/h north has a different velocity from a car driving 60 km/h south, even though their speeds are identical. The size of a velocity (ignoring direction) is the speed.

The key word in the definition is displacement. Displacement is the straight-line distance from the start point to the end point, together with the direction. It is not the same as total distance travelled. If you walk 5 m east and then 5 m back west, your distance is 10 m but your displacement is zero, so your average velocity is zero too.

The average velocity formula

The most common form of the velocity formula is the average velocity over an interval of time:

The standard SI unit is metres per second (m/s), but you will also see kilometres per hour (km/h), miles per hour (mph), and other distance-over-time units. As long as the top of the fraction is a length and the bottom is a duration, you have a valid velocity unit. To switch between distance units you can use a length converter, and the same idea underlies the average rate of change you may have met in algebra.

It helps to know a few common conversions so your answers land in the units a question expects. To go from metres per second to kilometres per hour, multiply by 3.6, so 5 m/s becomes 18 km/h. To convert the other way, divide by 3.6. For miles per hour, 1 m/s is roughly 2.24 mph. Here are the conversions you will reach for most often.

Velocity with constant acceleration

When an object speeds up or slows down at a steady rate, its velocity is not constant, so the simple displacement-over-time rule gives you only the average. To find the velocity at a specific moment under constant acceleration, use this equation of motion:

This says the final velocity equals the velocity you started with plus the extra velocity gained while accelerating. If acceleration is zero, the formula reduces to v = u, meaning velocity stays constant. To dig into acceleration itself, see the acceleration formula guide.

One practical tip: watch the sign of the acceleration. If an object is slowing down, its acceleration points opposite to its motion, so you plug in a negative value for a. For example, a ball thrown straight up with a starting velocity of 20 m/s feels gravity pulling it down at about 9.8 m/s squared. Using v = u + a x t with a as negative 9.8, the ball reaches zero velocity after roughly 2 seconds, which is the moment it stops rising and begins to fall. Choosing a consistent positive direction at the start of a problem and sticking with it is the surest way to keep these signs straight.

Velocity vs speed: the key difference

People use velocity and speed interchangeably in everyday talk, but in physics they are distinct. Here is a side-by-side comparison.

Because of these differences, average speed and average velocity are not always equal. On a round trip back to where you started, your average speed can be high while your average velocity is exactly zero, because displacement is zero.

Worked example: average velocity

A cyclist travels 150 metres east in 30 seconds along a straight road. Find the average velocity.

1. Identify the displacement: 150 metres east.
2. Identify the time elapsed: 30 seconds.
3. Apply the formula: v = displacement / time = 150 / 30.
4. Divide: 150 divided by 30 equals 5.
5. State the answer with direction: the average velocity is 5 m/s east.

Notice that the answer includes a direction. Leaving off the direction turns a velocity into a speed, which loses information.

Worked example: constant acceleration

A car starts at 10 m/s and accelerates at 2 m/s squared for 4 seconds. Find its final velocity.

1. List the values: u = 10 m/s, a = 2 m/s squared, t = 4 s.
2. Write the formula: v = u + a x t.
3. Multiply acceleration by time: 2 x 4 = 8.
4. Add the starting velocity: 10 + 8 = 18.
5. State the answer: the final velocity is 18 m/s.

Common mistakes to avoid

• Confusing distance with displacement. Average velocity uses displacement, the straight-line change in position, not the total path length.
• Dropping the direction. A velocity answer without a direction is incomplete; it has become a speed.
• Mixing units. Keep distance and time in matching units before dividing, for example metres with seconds, or convert first using a length converter.
• Using v = u + a x t when acceleration is not constant. That equation only holds for steady (uniform) acceleration.
• Forgetting that velocity can be negative. A negative sign simply means motion in the opposite direction to the one you chose as positive.

Good to know

Average velocity and instantaneous velocity are different. Average velocity covers a whole interval, while instantaneous velocity is the velocity at a single instant, which is what a car speedometer reads (as a speed). The two are equal only when velocity is constant. Because velocity is a rate of change, it is closely related to the slope of a position-versus-time graph, the same way the slope formula measures steepness on any line.