# Free tutorial in Basic Physics - Understanding Speed and Velocity

Understanding speed and velocity is helpful in understanding the physical phenomenons associated with the movement of the bodies. This article describes in detail and provides learnings about these entities.

### Introduction

In this basic Physics lesson, we will try to understand what is meant by speed and what is meant by velocity. We all know that when a body moves then we say that it has got some speed and it would travel or complete a distance in such and such time based on its speed. In our calculations for finding out the speed of a body, we can find the speed just by dividing the distance travelled by the time taken and we get the speed. So far we are not interested in the direction the body was moving. It could move in a straight path or a zig-zag path it is immaterial for us but in science when we talk about velocity then we are not only interested in finding the speed of a body but also its direction. That is where the velocity is different from the speed. A layman might use those two words indistinguishably but for a science student or a scientist, they mean quite different.

### Understanding speed

The speed of a body is a scaler quantity. It has no element of direction in it. It can be simply calculated using the formula speed = distance/time. For example, if a boy walks in a town from his house to the school through a maze of lanes and also the main road then the total distance travelled by him can be found by adding the length of those lanes and main road and once we know that distance then we can divide it by the time taken by him in that and we will get the speed of the boy. It is as simple as that. Speed can be uniform or it can vary and can increase or decrease. One can take a rest for a few minutes also on the way. If it is so then what we get by dividing the total distance by total time taken is called average speed. In most cases, we calculate the average speed only until we are sure that the body was moving at a constant speed.

Let us take one example of a person who has walked in the city market a total distance of 3.5 km (3500 m) in about 1 hour and 15 minutes. Now we can calculate his average speed by using the above mentioned basic formula. Let us calculate his average speed in the practical units which people understand easily and which is km/hr. The distance is 3.5 km and the time taken is 1 hour and 15 minutes which would be equal to 1.25 hours (you have to convert 15 minutes in hours and add to 1 hour). So, here the average speed is 3.5/1.25 = 2.8 km/hr. We can calculate the average speed in MKS units also that is in m/s (meters per second) and that would come as 3500/4500 = 0.78 m/s. In science the units are very important and changing the units will change the numerical value to a great extent and we have to be very careful in using the units correctly.

### Understanding velocity

Speed is a scalar quantity and when we add an element of direction to it then we have to divide the path of a body into small parts where the direction was not changing. Each part will be a vector quantity having a value as well as direction and that is the velocity in that part. To understand it better we will take an example of a person who goes from his house 120 metres in East direction and then turns northwards and walks 350 metres and then turns southwards and walks 600 metres and then turns westward and walks 450 metres and stops. Now each of these straight paths is the displacement that he had made in that direction and these displacements are all vector quantities as they have a value (equal to that distance) and they have also a direction. During these segments the direction of the speed was constant and this is in scientific terms is called velocity which has a value as well as a direction. So the value of the velocity will be the same as the value of speed at that point but now the element of direction is also added and so that combined entity is known as velocity. Always remember that velocity has an element of direction without which it is simply a speed at that particular point. In the above example, we can graphically draw the path of the person on a graph paper and find out where he is from his starting point and can measure it using the scale we have chosen to draw the path.

### Change in velocity

When a body is at rest and we apply a force on it then it would start moving and acquire a velocity. Now if we continue this force on the body the velocity of the body will increase and the rate of increase of velocity is proportional to this force applied. This rate of change or increase in velocity is known as acceleration. It is just like when we start our car and press our foot on the accelerator and its speed increases. If a body has a velocity of 'u' and after time 't' its velocity becomes v then we can find its acceleration 'a' by a simple formula like -
a = (v - u)/t that is rate of change of velocity.
Generally, this formula is written in the style v = u + at and the students generally remember it in that fashion only.
This is a very important formula and is used in calculations of velocities of a body under acceleration at different times.
Example:
Let us use this formula for finding out the velocity of a ball falling freely from the top of a twenty storey building say about 70 meters in height and the ball reaching the ground in about 4 seconds. In this case, the initial velocity is zero because we are not pushing it down but simply letting it go down under the gravitational attraction of the Earth. We also know that when a body falls freely under the gravity of the Earth then it has an acceleration of 9.8 metre/second square (g = 9.8 metre/second square). So let us use these values and find out the velocity v when the ball reaches Earth surface that is the ground level.
Here, we are given that u = 0, a = 9.8 metre/second square, and t = 4 seconds.
Putting these values in the formula v = u + at, we get v = 39.2 metre/second.
So the ball will strike the ground with this velocity v that is 39.2 metres/second. That is quite a good amount of velocity and depending upon the mass of the ball it could hurt a person badly if it falls on somebody's head.

### Relative velocities

The value of velocity perceived by an observer depends upon their relative positions. A person sitting in the train is not moving with respect to the train but an observer outside the train will see him moving along with the train and the velocity of the person sitting inside the train appears the same to the observer as that of the train. Another example is that Earth is moving with good speed around the Sun but we do not feel it because we are on Earth only and we cannot observe it as moving. At the same time, we can see the Moon (which is revolving around the Earth) moving across the sky above us.

### Conclusion

Knowing about speed and velocity is very useful in understanding the physical phenomenon associated with the movement of bodies. Speed is a scalar quantity and has a value. Generally in our real-life situations, we deal with average speeds. Velocity is a vector quantity and has a value as well as direction. The velocity of an object will increase or decrease depending upon the force and the direction of the force applied to the object. If a force is applied on a moving object in the opposite direction of its movement it would get decelerated and come to a stop. An observer perceives the velocity of an object depending upon the observer's position.

### Frequently Asked Questions

 Can we add two velocities?Yes, but velocity is a vector and the addition is to be done as per the vector addition. The result of addition will also have an element of direction which could even be different from the direction of those velocities. If we throw an object upwards will it always come back?When we throw an object upwards, it would come back but if we throw it with so much force that it acquires escape velocity and goes out of the Earth's gravitational field, then it does not come back. Why do not we feel the heavenly bodies moving, though they all have some velocity?Heavenly bodies are very far and our eyes cannot perceive their movement because of the limitations of perceptions of our eyes. However, we can perceive the satellites and other objects like aeroplanes, etc moving in the sky. Is acceleration also a vector quantity?Yes, it is derived from rate of change of velocity and that is a vector.

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