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With new discoveries and innovations constantly being made, the study of Physics Topics remains a vibrant and exciting field of research.

## What is Description of Motion in Physics

A tree is fixed at a place, so we say that it is stationary. Similarly, a house, a school, a factory, electric poles and telephone poles are all stationary objects which remain fixed at a place. On the other hand, a man, animals, birds, cars, buses, trains, ships and aeroplanes, etc., do not remain stationary all the time.

They can move from one place to another. For example, a man moves when he walks along a road, a bird moves when it flies in the sky, a cheetah moves when it runs in the jungle, and a fish moves when it swims in water.

Similarly, a car or bus moves on a road, a train moves on the track, a ship moves in water and an aeroplane moves when it flies in air from one place to another. The movement of a body (or object) is called motion. A common characteristic of all the moving bodies is that they change their position with time. We can now define motion as follows :

A body is said to be in motion (or moving) when its position changes continuously with respect to a stationary object taken as reference point. For example, when the position of a car changes continuously with respect to stationary objects like houses and trees, etc., we say that the car is moving or that the car is in motion. Let us take an example to understand the meaning of motion more clearly.

In Figure we see a car at position A in front of a house and a tree at a particular time (In this case, the house and tree are the stationary objects which are taken as a reference point). Now, after 5 seconds, we see the same car at position B which is quite far away from the house and the tree (see Figure).

This means that the position of this car is changing continuously with respect to a stationary object, house or tree. So, we say that this car is moving or that this car is in motion. Some other bodies (or objects) around us which show different kinds of motion are : swing (jhoola), merry-go-round, pendulum of a clock, and hands of a watch.

If a body moves fairly fast, then its movement (or motion) can be observed easily. But if a body moves very slowly, then it becomes difficult to observe its movement immediately. For example, a wrist watch has three hands : a seconds’ hand, a minutes’ hand and an hours’ hand, which move round and round on the dial of the watch.

Now, the seconds’ hand of a watch moves quite fast, so we can observe the movement (or motion) of the seconds’ hand of the watch very easily. But the minutes’ hand and hours’ hand of a watch move quite slow, so their movement cannot be observed easily.

We will have to keep on observing the position of minutes’ hand and hours’ hand for quite some time to find out whether they are moving or not. This is because when a body moves, its position changes with time.

In order to study the motion of bodies (or objects), we should first know the meanings of two terms : distance and displacement. These are discussed below. Another point to be noted is that in the study of motion, whether we use the term ‘body’ ‘or ‘object’, it means the same thing.

### Distance Travelled And Displacement

In everyday language, the words distance and displacement are used in the same sense but in physics these two words have different meanings. Let us understand this difference by taking an example.

Suppose a man lives at place A (Figure) and he has to reach another place C, but first he has to meet his friend living at place B. Now, the man starts from point A and travels a distance of 5 km to reach B, and then travels another 3 km from B to reach C.

Thus, the man goes along the path ABC (shown by dotted lines). Length of the path ABC gives us the actual distance travelled by the man. Thus, the distance travelled by a body is the actual length of the path covered by a moving body irrespective of the direction in which the body travels.

For example, in this case, the actual length of the path covered by the man is 5 km + 3 km = 8 km, so the distance travelled by the man is 8 km.

We will now discuss this problem in a different way. When the man has Displacement = 4 km towards East, reached point C, we want to know how far he is now from the starting point A, that is, we want to know the shortest distance between point A and point C.

Let us draw a straight line AC between A and C. The length of the straight line path AC (which is 4 km here) is the displacement of the man from point A, that is, on reaching C, the man is only 4 km away from the starting point A. This displacement is in the East direction.

Thus, when a body moves from one point to another, the distance travelled refers to the actual length of the indirect path whereas displacement refers to the straight line path between the initial and the final positions. So, whatever be the actual length of the path followed by a moving body, displacement of the body is always represented by the shortest distance between the initial and final positions of the body.

Thus : When a body moves from one position to another, the shortest (straight line) distance between the initial position and final position of the body, alongwith direction, is known as its displacement. In the above example, the shortest distance between the initial position A and final position C of the man is 4 km, so the displacement of man is 4 km in the East direction. It is clear that the distance travelled has only magnitude whereas displacement has magnitude as well as direction.

The quantities like distance, displacement, etc., are known as physical quantities (or quantities of physics). The magnitude of a physical quantity means size of the physical quantity. A physical quantity having only magnitude (or size) is known as a scalar quantity. A scalar quantity has no direction. On the other hand, a physical quantity having magnitude as well as direction is known as a vector quantity.

- Distance is a scalar, quantity (because it has magnitude only, it has no specified direction).
- Displacement is a vector quantity (because it has magnitude as well as a direction).

For example, if a car travels a distance of 50 km, then the expression “50 km” is the distance travelled, and if the car is travelling in a straight line in the East direction (or any other direction), then the expression “50 km towards East” is the displacement of the car.

The distance travelled by a moving body cannot be zero but the final displacement of a moving body can be zero. The displacement of a moving body will be zero if, after travelling a certain distance, the moving body finally comes back to its starting point (or starting position).

This will become clear from the following examples. Suppose a man starts from place A and travels a distance of 5 km to reach place B [see Figure 5(a)], From place B he travels another 3 km and reaches place C. And finally the man travels 4 km from place C to reach back to the starting point A [see Figure(a)]. In this case, though the man has travelled a distance of 5 km + 3 km + 4 km = 12 km, but the final displacement of the man is zero.

This is because the man has reached back at the starting point A and the straight line distance between the initial position A and final position A is zero. Thus, if we take a round trip and reach back at the starting point then, though we have travelled some distance, our final displacement will be zero.

This is because the straight line distance between the initial and final positions will be zero. For example, if we travel along a circular track of radius r and reach back at the starting point A [see Figure (b)], then though we have travelled a distance 2πr (equal to circumference of track) but our final displacement will be zero. We will now solve a problem based on distance and displacement.

**Example Problem.**

A man travels a distance of 1.5 m towards East, then 2.0 m towards South and finally 4.5 m towards East.

(i) What is the total distance travelled ?

(ii) What is his resultant displacement ?

**Solution:**

(i) Total distance travelled = 1.5 + 2.0 + 4.5

= 8.0 m .

(ii) To. find the resultant displacement we should draw a map of the man’s movements by choosing a convenient scale. Let 1 cm represent 1 m. Then 1.5 m can be represented by 1.5 cm long line, 2.0 m by 2.0 cm line and 4.5 m by a 4.5 cm long line.

We draw a 1.5 cm long line AB from West to East to represent 1.5 m towards East (see Figure). Then we draw a 2.0 cm long line BC towards South to represent 2.0 m towards South. And finally we draw a third line CD, 4.5 cm long, towards East to represent a distance of 4.5 m towards East.

Now, the resultant displacement can be found by joining the starting point A with the finishing point D. Thus,, the line AD represents the final displacement of the man. Let us measure the length of line AD. It is found to be 6.3 cm.

Now, 1 cm = 1 m

So, 6.3 cm = 6.3 m

Thus, the final displacement as represented by AD is 6.3 metres.

Please note that whenever a body travels along a zig-zag path, the final displacement is obtained by joining the starting point and the finishing point of the body by a straight line.

### Uniform Motion And Non-Uniform Motion

A body has a uniform motion if it travels equal distances in equal intervals of time, no matter how small these time intervals may be. For example, a car running at a constant speed of say, 10 metres per second, will cover equal distances of 10 metres, every second, so its motion will be uniform. Please note that the distance-time graph for uniform motion is a straight line (as shown in Figure).

A body has a non-uniform motion if it travels unequal distances in equal intervals of time. For example, if we drop a ball from the roof of a tall building, we will find that it covers unequal wjstudygear distances in equal intervals of time. It covers :

4.9 metres in the 1st second,

14.7 metres in the 2nd second,

24.5 metres in the 3rd second, and so on.

Thus, a freely falling ball covers smaller distances in the initial ‘1 second’ intervals and larger distances in the later ‘1 second’ intervals (see Figure).

From this discussion we conclude that the motion of a freely falling body is an example of non uniform motion. The motion of a train starting from the Railway Station is also an example of non uniform motion. This is because when the train starts from a Station, it moves a very small distance in the ‘first’ second.

The train moves a little more distance in the ‘2nd’ second, and so on. And when the train approaches the next Station, the distance travelled by it per second decreases. Please note that the distance-time graph for a body having nonuniform motion is a curved line (as shown in Figure).

Thus, in order to find out whether a body has uniform motion or non-uniform motion, we should draw the distance-time graph for it. If the distance-time intervals of time. So, it has non-uniform motion. graph is a straight line, the motion will be uniform and if the distance-time graph is a curved line, the motion will be non-uniform. It should be noted that non-uniform motion is also called accelerated motion.