In our daily life speed and velocity are something we must encounter moving from one place to another gives us the ability to actuate these two terms. Speed and velocity are related in such a way that distance and displacement are related. Speed is a scalar and velocity is a vector. The *v* (italic) is the symbol of speed while velocity gets the symbol **V** (boldface). Also, average values get a bar over the symbol. In this article, you will have in-depth knowledge of the definition, formula, units, symbols, and examples of speed and velocity. You’ll also learn the difference between speed and velocity.

Read more: Understanding distance and displacement

Contents

## What is speed?

Speed simply refers to the time rate at which an object traveled a certain distance. we can also say speed is how fast an object Moves to cover a distance. Speed is known as a scalar quantity, it is only magnitude. When two identical objects are traveling at different speeds, what is their difference? Their difference is just that one is traveling faster (the one with the greater speed) and will go farther than the one moving slower in the same amount of time. This also tells that the object moving faster will get to its destination faster than the object moving slower.

At whatever speed, it involves both distance and time. And “Faster” describes greater distance or Farther and Sooner means less time. Increasing one’s speed means doubling one’s distance traveled in a given amount of time. It also means having the time required to travel a given distance. These statements are common and useful in mathematics. The symbol *v in* italic is used for speed due to the association between speed and velocity:

- Speed is directly proportional to distance when time is constant: v ∝s (t constant)
- Speed is inversely proportional to time when distance is constant: v ∝
^{1}t (s constant)

When we combine these two rules, we get the definition of speed in symbolic form. Although, this is not the final definition.

v = | s |

t |

Here is another way to define speed without using symbols. Speed is the rate of change of distance with time.

Read more: Understanding acceleration

Let quickly take a calculation on speed but to achieve that, we must know how far it’s gone and how long it took to get there. although “Farther” and “Sooner” correspond to “Faster” note that! Let assume you drove a car from New York to Chicago. The distance by road is roughly 300 km (200 miles). If the journey takes four hours, what is the speed at which you traveled?

Applying the above formula, we get

v = | s | ≈ | 300 km | = 75 km/h |

t | 4 hours |

The number calculated above is not the speed of the car but the average speed of the entire journey. To emphasize this point, the equation can sometimes be modified as follows:

v = | ∆s |

∆t |

The bar over the v means an average or a mean and the ∆ (delta) symbols describe a change. It can see as “vee bar is delta ess over delta tee”. This is the quantity we calculated for our hypothetical trip. In contrast, a car’s speedometer shows its instantaneous speed, that is, the speed determined over a very small interval of time – an instant. Normally, this interval should be as close to zero as possible, however, in reality, we are limited by the sensitivity of our measuring devices. But it is possible to imagine calculating average speed over smaller time intervals until we have effectively calculated instantaneous speed. This can be written symbolically as:

v = |
| ∆s | = | ds | ||

∆t | dt |

Read more: Understanding buoyancy

With those familiar with calculus, calculus speed is the first derivative of distance to time. Well, this is not something to worry about if you haven’t dealt with calculus. There are other simpler ways you can find the instantaneous speed of a moving object. On a distance-time graph, speed corresponds to slope and thus the instantaneous speed of an object with non-constant speed can be found from the slope of a line tangent to its curve. This will be discussed in another topic.

## What is velocity?

Velocity simply means the rate at which an object changes its position. Velocity is a vector quantity; it has both magnitude and direction. for instance, an object moving quickly and still in its original position. Let say the object is moving forward with 2 Meter and at the same time moving backward with the same amount of speed 2 meters, that shows that the person is moving with no/zero velocity, but an object moving forward with the speed of 2m/s, such an object is moving with velocity, and velocity is the rate in which an object changes its position because the position of that object is changing with 2meters every second.

The calculation of velocity can be achieved by knowing how far the object is gone and how long it took to get there. you then have to know whether distance or displacement is needed or whether the speed or velocity is what to be calculated. Here,

- Average speed is the rate of change of distance with time.
- Average velocity is the rate of change of displacement with time.

And for calculus,

- Instantaneous speed is the first derivative of distance to time.
- Instantaneous velocity is the first derivative of displacement with respect to time.

In essence, speed tells you how fast, while velocity tells you how fast and also determines the direction.

Read more: Relationship between Force and Motion

## Units

Speed and velocity are both measured using the same units. For distance and displacement, their SI unit is a meter, while for time, the SI unit is second. The SI unit for speed and velocity is a meter per second. This unit is often used outside scientific and academic circles. Most people measure speeds in kilometers per hour (km/h or kph). The United States uses the older mile per hour (mi/h or mph).

## Differences between speed and velocity

The table below shows the difference between speed and velocity.

## Speed | ## Velocity | ||

1. | Speed is the time rate at which an object traveled a certain distance | Velocity is the rate at which an object changes its position | |

2. | Speed is a scalar quantity; it has magnitude and no direction | Velocity is a vector quantity; it has both magnitude and direction | |

3. | Speed is always positive | Velocity is either positive, negative, or zero | |

4. | Speed SI unit is in m/s | Velocity SI unit is in m/s |

Read more: How Force changes the State of Motion

#### Watch the video below to learn more about speed and velocity.

## Examples of speed and velocity

Below are the examples of speed and velocity:

- Device, event, phenomenon, process
- Human sperm cells
- Hair growth, fingernail growth
- Snails
- Pouring ketchup from its bottle
- Cockroaches
- Sloths, tortoises, turtles.
- Ocean currents.
- Human, typical walking pace.
- Fastest human – Swimming (Cesar Cielo).
- Maximum comfortable elevator speed.
- Dolphins, porpoises, whales.
- Falling raindrops.
- Fastest human – running (Usain Bolt).
- Stadium wave.
- Champagne cork.
- Rabbits, hares, horses, greyhounds, tuna, sharks.
- Cheetahs
- Falling hailstones.
- Peregrine falcon in a dive.
- Very fast golf ball.
- Hurricane, maximum sustained wind speed.
- Tornado, maximum sustained wind speed.
- Commercial jet airplane.
- Speed of sound in air, STP.
- Speed of sound in water.
- Seismic waves.
- Fastest airplane (SR-71 Blackbird).

Read more: Forms of energy: kinetic and potential energy

## Conclusion

Speed and velocity are something we must encounter moving from one place to another give us the ability to actuate these two terms. Speed is how fast an object Moves to cover a distance and is known as a scalar quantity. Velocity is the rate at which an object changes its position and is a vector quantity. That is all for this article, where the definition, formula, units, symbols, examples, and difference between speed and velocity are being discussed.

I hope you gained a lot from the reading, if so, kindly share with other students. Thanks for reading, see you next time.