Velocity and acceleration both describe motion, but there is an important difference between the two. If you’re studying physics at high school or college level, understanding the differences between them is essential. Understanding what velocity means leads to an understanding of what acceleration means because while velocity is the rate of change of position, acceleration is the rate of change of velocity. If you’re traveling at a constant pace, you have velocity but no acceleration, but if you’re traveling and your pace is changing, you have velocity and acceleration.

#### TL;DR (Too Long; Didn't Read)

Velocity is the rate of change of position with respect to time, whereas acceleration is the rate of change of velocity. Both are vector quantities (and so also have a specified direction), but the units of velocity are meters per second while the units of acceleration are meters per second squared.

## What Is Velocity?

The rate of change of your position with time defines your velocity. In everyday language, velocity means the same thing as speed. However, in physics, there is an important distinction between the two terms. Speed is a “scalar” quantity, and it’s measured in units of distance/time, so in meters per second or miles per hour. Velocity is a “vector” quantity, so it has both a magnitude (the speed) and a direction. Technically, saying you’re traveling at 5 meters per second is a speed and saying you’re traveling at 5 meters per second towards the north is a velocity, because the latter has a direction too.

The formula for velocity is:

*Velocity = distance traveled ÷ time taken*

In the language of calculus, it can be more precisely defined as the rate of change of position with respect to time and so is given by the derivative of the equation for position with respect to time.

## What Is Acceleration?

Acceleration is the rate of change of velocity with time. Like velocity, this is a vector quantity that has a direction as well as a magnitude. An increase in velocity is commonly called acceleration while a decrease in velocity is sometimes termed deceleration. Technically, since velocity includes a direction as well as a speed, a change in direction at a constant speed is still considered acceleration. Acceleration can be defined simply as:

*Acceleration = change in velocity ÷ time taken for velocity to change*

Acceleration has units of distance/time squared – for example, meters/second^{2}.

In the language of calculus, this is more precisely defined as the rate of change of velocity with respect to time, so it’s found by taking the derivative of the expression for velocity with respect to time. Alternatively, you can find it by taking the second derivative of the expression for position with respect to time.

## Constant Acceleration vs. Constant Velocity

Traveling with a constant velocity means you’re going at the same speed in the same direction continuously. If you have a constant velocity, this means you have zero acceleration. You can imagine this as driving down a straight road but keeping your speedometer on the same value.

A constant acceleration is quite different. If you travel with a constant acceleration, your velocity is always changing, but it’s changing by a consistent amount each second. The acceleration due to gravity on the Earth has the constant value 9.8 m/s^{2}, so you can imagine this like dropping something from a skyscraper. The velocity starts low, but increases by 9.8 m/s for every second it is falling under gravity.

## Acceleration and Newton’s Second Law

Acceleration, rather than velocity, forms a key part of Newton’s second law of motion. The equation is *F* = *ma*, where *F* stands for force, *m* is mass, and *a* is the acceleration. Because of the link between velocity and acceleration, you can also write this as *force = mass × the rate of change of velocity*. However, acceleration is the key characteristic here, not velocity.

## Velocity and Momentum

The equation for momentum uses velocity instead of acceleration. Momentum is *p* = *mv*, where *p* is momentum, *m* is mass, and *v* is velocity. In Newton’s second law, acceleration multiplied by mass gives force, whereas when velocity is multiplied by mass, this gives the momentum. Their definitions are different, and this shows how those differences lead to distinct equations in practice.