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Displacement Calculator

Displacement is the term that tells by how much an object moved. Now you may come up with a doubt asking is that not what the term ‘distance’ says? Yes, the terms distance and displacement are oft confused and used interchangeably.

Here is a comprehensive explanation about displacement and distance, how they are different and how to calculate them easily.

What is displacement?

Consider the diagram given below.

Displacement Triangle

Assume that a particle moves from A to B via C as shown here. Then the net distance that it travelled is 3+4 which is 7 meters. But if you take a keen look, the shift that it underwent from A to B is 5m, had it travelled in the straight path between A and B, without going through C.

Thus, 7 meters is the total ‘distance’ the particle travelled, while 5 meters is the total ‘displacement’ it underwent in its position.

So now it is clear that:

  • Distance is the total length travelled by a particle from its initial position, while
  • Displacement is the shortest length between its initial point to the final point.

On a keen observation, we notice one commonality in between these two terms – Both have the same ‘initial point’ as a reference to their measurement.

What else do you need to know about distance and displacement?

Distance can be always positive; while displacement can be zero, positive or negative. Confused how? Let’s see.

Consider the case of particles travelling in the form of a uniform wave. Every particle moves a certain distance from the mean position up and down or in positive and negative directions. Thus, after the particle completes one full cycle, the net displacement of the particle from the mean position is zero. But, it has travelled a distance equal to one wavelength.

Consider another example as shown below:

Displacement Rectangle

If a particle started from A and travels through B, C and D in the clockwise direction and again reaches A, then:

The total distance it travelled is the perimeter of the rectangle as shown, i.e., 10 + 5 + 10 + 5 = 30m

The total displacement of the particle from its initial position is Zero because it finally reached the place where it started from.

How about if it travels in the upward direction to A for a distance of 5m? Then its final displacement would be -5m. Yes. Thus displacement is dependent on direction or a vector quantity.

How about the distance in this case? It would be 30 + 5 = 35m. It means distance is not dependent on direction or it is a scalar quantity. It is only the sum of the total lengths of the paths in which the particle travels, irrespective of the direction.

The shortest distance between two points is a straight line. – Archimedes

Key points about Distance and Displacement
  • Distance is the actual length that a particle travelled from its initial point.
  • Displacement is the net length that the particle travelled between its starting and final points.
  • Displacement can be equal, greater than or lesser than distance.
  • To calculate displacement, you need a reference point. Because it is with respect to that point, the displacement is calculated. But for calculating distance, no reference points are needed.
  • Distance can be covered by travelling on any path between two given points. But displacement is only one unique path between the two given points.
  • Distance is a scalar quantity and is represented as ‘d’ and displacement is a vector represented by ‘s’.
  • Numerically, to calculate distance, you can multiply speed and time taken; while to obtain displacement, you need to multiply velocity and time.
  • When you know distance, you can have the idea of the path in which the particle travelled. But with the help of displacement value, you can never find out the path that the particle has travelled to reach its final point.

Did you know?

Displacement in physics is represented in shorthand as Δs. Well, there is an interesting fact behind this. While Δ (delta in Greek) represents the change or the difference between two quantities, s represents the spatial distance covered. That is Δs represents the change in spatial distance that a particle undergone. Hence the reason displacement is represented by s or Δs to be precise.

Time is the longest distance between two places.

What is the formula to calculate displacement?

The displacement of a particle is calculated by using the formula: s= ½ (v+u) x t,
Where s is the displacement
V is the final velocity in m/s
U is the final velocity in m/s
T is the time taken to travel from initial to final position, in seconds.

How CalculatorHut’s displacement calculator helps you?

Students find the calculation of displacement indispensable as a part of their assignments. CalculatorHut’s online free displacement calculator will help in calculating displacement easily. They can also cross verify the results that they have done manually.

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