# Difference Between Speed and Velocity

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## Introduction

Speed and velocity are very common terms in the study of motion. Most people use it interchangeably in everyday usage, but both have different meanings. Speed is defined as the rate of distance covered by a body or an object, whereas velocity is also defined as the same but has a direction associated with it. In everyday usage, we are very familiar with both words but do we all know the correct difference? The difference has already been proved by mathematics and physics. And in this article, we are going to do a deep study and see why velocity and speed are not the same.

## Speed vs. Velocity

The main difference between speed and velocity is that speed does not specify a body moving in any direction while velocity specifies a body moving with a certain speed in a particular direction. The quantities which include both speed and direction of a body than those quantities are known as vector quantities, while the quantities which do not include direction are known as scalar quantities.

The distinction is important because of things like opposite directions and relationships with other quantities like acceleration, which is also associated with the direction of the body.

The directions are major because we must know where the body will head. Therefore, defining speed and velocity as separate quantities is of critical importance in physics and mathematics to understand the motion of bodies.

## What is Speed?

Speed can be defined as the rate at which a distance is covered. It also tells us how fast or slow an object or a body can cover a particular distance.

Speed is stated by keeping both distance and time in mind. It changes and interdepends upon both distance and time.

Speed is a scalar quantity, which states "how fast a body can travel." The above-stated line makes it obvious that a fast-moving object can cover a large distance in a small time, whereas a slow-moving object will take a large amount of time to cover the same distance.

Therefore, speed is a key term used in our daily lives and how often we are habituated to using this term.

Speed= distance/time

Where distance can be in metres, kilometres or miles and time can be in seconds, minutes or hours.

Speed can be expressed in various units such as metres per second (m/s), kilometres per hour(km/hr.), and miles per hour(mph). The Units are availed in different contexts or situations.

It is also defined as the magnitude of velocity, where velocity is a vector quantity. As used earlier, that speed is a scalar quantity. Then a question arises in every mind, what does a scalar quantity mean?

Scalar quantities are those quantities, that are only associated with magnitude and no direction. More precisely, quantities with only numerical value without direction Examples of scalar quantities are mass, force, distance, speed, time and vice versa.

There are many more deductions physics has made about speed. We will understand that by classifying it into various types,

### Based on Uniformity

1. Uniform speed- A body that travels an equal distance in the same interval of time, then the body is said to be following uniform speed.  In the distance-time graph, we show uniform speed through a straight line.
2. Non-uniform speed (or variable speed)- A body that does not travel an equal distance in the same amount of time is said to be in non-uniform speed. It is shown by any curve which does not change uniformly throughout the distance-time graph.

### Other important types of speed are:

#### Instantaneous Speed

When the speed of the body, is recorded at any instant,  or speed gathered over a shorter period is known as Instantaneous Speed.

For example, the speed that is shown on a vehicle’s speedometer at any instant is the instantaneous speed of the body.

The other example of instantaneous speed is a basic thing that we keep on going back to, i.e., typing speed.

Typing speed is calculated based on how many words one can type in a minute. It gives the instantaneous speed of that interval. And, if you consider the instantaneous speed of my writing this article, then you would get how it is going to take me an eternity to complete this one.

Let us move to Average speed. What does it say?

#### Average Speed

It is the rate of total distance travelled by a body or an object. Putting it more simply, it is the mean of all the instantaneous speeds considering at all intervals.

It also tells you the average rate at which it will cover the given distance. It gives the average value of speed, around which the whole distance was covered.

Average velocity=total distance/total time

If a body travel d1+d2+d3………… distances, with s1+s2+s3………. Speeds. Total time taken will be d1s1+d2s2 +....…

If the total distance travelled is d1+d2+d3.

The total time taken= d1s1+d2s2+d3s3

The average speed= d1+d2…………/d1s1+d2s2+…

If the vehicle travels equal distances at different speeds, then

Average speed= 2s1s2s1+ s2

Here, the Average Speed is the harmonic mean of individual speeds.

#### Relative Speed

If two bodies are moving towards each other or in relative motion to each other, then according to the concept of Relative Speed, i.e.,

Relative speed=v1+v2

If they travel in the same direction, then the relative speed will be:

Relative speed=v1-v2

## What is Velocity?

Velocity gives somewhat the same idea as speed, that how fast or slow an object can move, but in the case of velocity, there is something more associated with it, i.e., direction. As velocity is a vector quantity, it must have both magnitude and direction associated with it.

Vector quantities are those quantities which require both magnitude and direction. More precisely, both the numerical value and direction of the given object’s motion. For where the given object will head at a certain amount of speed.

For example, if two bodies move with the same magnitude and in opposite directions, then we need one quantity to tell the difference between two bodies moving in opposite or different directions, that is when the term velocity was defined.

Car A moves towards the south at 40 km/hour, whereas car B moves towards the north at the same speed. Both cars will have the same magnitude but in different directions. And that is when velocity comes into the picture to define the given situation.

Velocity is essential to define the motion of objects. In various contexts, from one-dimensional motion to two-dimensional motion or three-dimensional motion. Velocity is vital in fields like engineering, navigation, astronomy, and vice versa, where accurate measurement is of utmost importance.

### Relative Velocity

Relative velocity is a type of velocity where we bring two different velocities into a single coordinate system. Relative velocity is fundamental in modern physics since its use in relative motion is necessary. In Newtonian Mechanics, the relative velocity is independent of the chosen frame, whereas Special Relativity depends upon the inertial frame.

For example, if you take object A moving with velocity 'u' and object B moving with velocity 'v'.

The velocity of A relative to B,

vA relative to B=u-v

Similarly, the Velocity of B in respect of A,

vB relative to A=v-u

To find the Relative Velocity of the given two objects, the inertial frame stays at rest.

### Average Velocity

The concept behind average velocity is the same as average speed, but here we take displacement instead of distance. Displacement depends upon the direction.

The average velocity is always less than or equal to the average speed, as displacement can increase or decrease in magnitude and direction.

### Relation With Acceleration

Acceleration is defined as the derivative of velocity concerning time, i.e.,

a=dvdt

The above expression says that from the slope of the velocity-time graph, we get acceleration.

Then, we can also derive an expression for velocity from the acceleration-time graph, where the area under the curve gives the velocity, i.e.,

v=a.dt

### In the Case of Constant Acceleration

The acceleration is constant when velocity changes at a uniform rate. Similarly, if acceleration is zero, velocity does not change. If acceleration is positive, velocity increases. If acceleration is negative, velocity decreases.

### Quantities That Depend On Velocity

Kinetic Energy- The kinetic energy of a moving object is dependent upon its velocity and it is given by the equation is:

K.E=12mv2

Where m is the mass and v is the velocity.

Momentum- Momentum is measured as the product of mass times velocity. It is denoted by p.

p=m.v

Escape Velocity-It is the minimum velocity required by an object to escape the Earth.  It represents the kinetic velocity of the object and it is given by the expression:

vescape=2G.Mr

Where G is the gravitational constant, r is the radius of Earth and M is the mass of Earth.

These were some of the quantities that depend upon velocity.

Now, we will move on to the main difference between speed and velocity.

## Main Differences Between Speed And Velocity in Points

• Speed deals only with magnitude, i.e., a scalar quantity, whereas Velocity gives us both magnitude and direction, i.e., a vector quantity.
• Speed is a quantity that changes with the distance travelled by an object in a period and at the same time ignores the direction, whereas, velocity changes with displacement travelled by an object over a period.
• Both quantities are measured in distance per unit of time, but in the case of velocity, we consider the direction of motion in a given time.
• Velocity is always considered to be an average quantity, as we measure the distance over a specified time. Whereas, speed can be Instantaneous or average, as we measure either over a specified time or a duration of time.

## Conclusion

As you have understood, we have been discussing the motion of bodies where distance, displacement and time are essential. It is when physicists derived basic quantities like speed and velocity to understand the motion of bodies more clearly.

Mathematical calculations of speed are straightforward, whereas the calculations of velocity are a little difficult. Because in velocity we involve calculus. The term speed is used very often on roads, so that is what speed a vehicle should maintain to safely drive through. And, velocity is used mostly in science to make calculations simpler, as it gives us the information of direction.

Therefore, both quantities are vital to explain the motion of bodies and without this, it is impossible to study kinematics.

• Speed vs Velocity: What's the Difference & Why It Matters (w/ Examples) | Sciencing What's the Difference Between Speed and Velocity? | Britannica
• Velocity - Wikipedia