# What Is the Formula for Velocity?

By: Mark Mancini  |

Key Takeaways

• Speed and velocity are distinct concepts; while speed only considers the magnitude of movement, velocity also takes into account the direction.
• The formula for velocity is given by velocity (v)=displacement (d)time (t)velocity (v)=time (t)displacement (d)​, where displacement is the distance covered in a specific direction.

Far be it for us to criticize speeding tickets as a public safety tool (and a source of municipal revenue), but maybe law enforcement officials should think about renaming them "velocity tickets."

Allow us to make our case. You see, while the two concepts are related, the words "speed" and "velocity" do not, however, in physics, refer to the same thing.

Contents

## Velocity, Defined

Speed is the total distance over which an object travels during a particular interval of time.

Velocity adds something else to the conversation. Being what physicists call a "vector quantity," velocity incorporates both magnitude and direction. On the other hand, speed is a "scalar quantity," a phenomenon that deals with magnitude — but not direction.

Michael Richmond, Ph.D., professor at Rochester Institute of Technology's School of Physics and Astronomy, defined velocity as "the rate at which displacement changes with time."

## Covering Ground

What, pray tell, is "displacement?" Basically, this marks an object's change in position or the difference between where it physically started and where it ends up.

Note that the change in an object's position is not always equal to the distance it's traveled. That might sound counterintuitive, but bear with us.

Run one lap in a perfect 8-foot (2.4-meter) circle and you will have covered a distance of 8 feet.

However, you will also have circled right back to your original starting point. So that means your displacement will be equal to 0 feet (i.e., 0 meters), even though you traveled a greater distance.

## Learning By Example

Time for another hypothetical.

Let's say you're at the gym making small talk. If another patron were to tell you "Gary sprinted 39.3 feet (12 meters) in three seconds today," they'd be giving you his speed, but not his velocity.

To calculate Gary's velocity, we'd need more information.

If our gym buddy said, "Gary sprinted 39.3 feet (12 meters) west in three seconds today," then we'd know about his direction of travel and be off to a good start.

The formula for calculating an object's velocity is as follows:

v = d/t

Here, the letters "v," "d" and "t" respectively denote "velocity," "displacement" and "time." In other words, velocity = displacement divided by time.

When using this formula, it's important to measure displacement in meters and time in seconds. For simplicity's sake, let's assume that old Gary ran to the west in a perfectly straight, 12-meter (32.8-foot) line, so his displacement equals the distance he traveled.

We also know that it took him three seconds to cover the gap between his starting and ending points.

Therefore, when we plug in the numbers, we get this:

v = 12/3

Ergo, westbound Gary had an average velocity of 4 meters per second (13.12 feet per second).

(Phrasing matters here. All we've done is calculate Gary's average velocity; we haven't addressed the subject of instantaneous velocity, a phenomenon that puts its own twist on the formula broken down above.)

## Velocity Formula Calculator

Now ... about those so-called "speeding" tickets. If you've ever received one, the direction in which your vehicle was headed at the time must've been a factor. Consciously or not, it's something both you and the police officer considered.

Know what's worse than driving way too fast? Driving way too fast in an illegal direction. (Consider one-way streets. Or even two-lane roads that force the motorists on one side to travel at a slower pace.)

So yeah, given all we've learned today, we think you could make the case that "speeding tickets" should really be called "velocity tickets." Or something similar. Good night, everybody.

### Frequently Asked Questions

##### How does air resistance affect an object's velocity?
Air resistance, also known as drag, can significantly alter an object's velocity by opposing its motion. The faster an object moves, the greater the air resistance it encounters. This force must be factored in when calculating an object's velocity in air, as it can decrease the object's speed and alter its direction, making the velocity vector smaller and sometimes changing its orientation.
##### Can velocity change if speed remains constant?
Yes, velocity can change even if speed remains constant because velocity is a vector quantity that includes both speed and direction. If an object moves at a constant speed but changes its direction, its velocity changes. This is often seen in circular motion, where the speed may stay the same, but the direction (and thus the velocity) is constantly changing.
##### How does air resistance affect an object's velocity?
Air resistance, also known as drag, can significantly alter an object's velocity by opposing its motion. The faster an object moves, the greater the air resistance it encounters. This force must be factored in when calculating an object's velocity in air, as it can decrease the object's speed and alter its direction, making the velocity vector smaller and sometimes changing its orientation.
##### Can velocity change if speed remains constant?
Yes, velocity can change even if speed remains constant because velocity is a vector quantity that includes both speed and direction. If an object moves at a constant speed but changes its direction, its velocity changes. This is often seen in circular motion, where the speed may stay the same, but the direction (and thus the velocity) is constantly changing.