Position, Path Length and Displacements

What are the Position, Path Length, and Displacement?

But before we move forward let us know what is motion. If we look around, everywhere we can see objects moving. Kids play, birds fly, animals move for the search of food, people walk or run, vehicles run on the road, river flow, etc. So basically, we can find motion everywhere in the universe. But what is meant by motion?

If you notice the above-mentioned instances they all move from one place to another and change their place. Therefore, motion is nothing but the process or act of moving and changing in the direction of an object with time.  If a body is at rest, it means that the body is not in motion, merely means that it is being described concerning a frame of reference that is moving together with the body Position


Position

To describe the motion of an object, you must know and be able to describe its position.

Let us understand this with an example, let us say Ram moved from point R to S. Which means Ram's initial/previous position was R from where he shifted to S. Now the question is how we can represent Ram's initial position? In physics, we specify a position with the help of a reference point and a set of three mutually perpendicular axis or the rectangular coordinate system. They are the X, Y, and Z-axis. The reference point is known as origin; it is the intersection of the above three-axis (X, Y, and X). So we take point R as the reference point or origin with coordinates (0, 0, 0) and S is represented by a set of coordinates on the three-axis (X, Y, Z).

Since we know that motion is the change in position with time, we install a clock in this system. The coordinate system along with the clock is the frame of reference. A frame of reference is an arbitrary set of axes from which the position and motion of the object are described. Thus, if one or more co-ordinates of a body change with time, the body is said to be in motion.


Path Length

The path length is the actual length of the path traversed by the body between the Initial and Final position.


Displacement

It is the shortest length i.e. Straight line distance between Initial and Final positions. Displacement is a vector quantity 

Since displacement has magnitude and direction, it is a vector quantity and the path is a scalar because it has only and no direction


Explanation with Examples

To have a proper understanding of the position, path length, and displacement and the difference between them. Follow are some examples given with explanation:

Let us take three examples here. In the first one, Ram starts traveling from point R of the square path RSTU with RS = 1 km. He travels through S, T, U, and comes back to A in 20 minutes. The distance traveled by him is 4 x 1 km = 4 km. But if you see the change in his position from the start to the end of the journey, it is nil (It has no change). Ram started at the point R and came back at R.

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In the second example, 

Ram travels from Point R to S along the straight line in 60 minutes. The distance traveled by him is 5 km. And the total distance from the start to the endpoint traveled by Ram is also 5 km.

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Now in the third example, Ram travels through the triangular path. He starts from point R and reaches T through point S in 120 minutes. The distance that has been traveled by him is 3 km + 4 km = 7 km. But if we see how far he is from the point where he started his journey, it is 5 km.

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If you notice the above examples, the distance traveled and the change in position may or may not be the same.

The distance traveled by the body is known as the path length. Whereas the change in position, that is the difference between the initial and final positions of the body is called its displacement.

Hence, the path length is 4 km but the displacement is 0 in the first case.  The path length is the same as the displacement – 5 km in the second example and the third example, the path length is 7 km but the displacement is 5 km.

FAQ (Frequently Asked Questions)

1. What are The Differences and Similarities Between Path Length And Displacement?

Differences

  • Path length is the actual length of the path traveled by the body between initial and final positions. And the displacement is the shortest distance between the initial and final positions

  • The path length is a scalar quantity but the displacement is a vector quantity.

  • The magnitude of path length can never be 0 or negative but not in the case of displacement, it can be 0 or negative.

  • The displacement of a body can never be greater than the distance covered, it can either be equal or lesser than the distance covered.


Similarities

  1. Both of them have the same SI unit.

  2. When the body moves in a straight path, the distance and displacement are equal.

2. What is Motion?

The Phenomenon in which an object changes its position over time is known as motion.   Mathematically motion is described in terms of displacement, distance, velocity, acceleration, speed, and time. By attaching a frame of reference to an observer and measuring the change in position of the body relative to that frame with a change in time we can measure the motion of a body

Motion can be applied in various physical systems like - objects, bodies, matter particles, matter fields, radiation, radiation fields, radiation particles, curvature, and space-time.  Therefore, the term motion, in general, signifies a continuous change in the positions or configuration of a physical system in space.