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Displacement

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The displacement tells a lot about motion. Lets have a pictorial illustration about it. A runner running in her track returns to the same position where she left. Even though she runs for 1000 m since she reaches the same point at the end her displacement is zero
Displacement

This with clarity tells that displacement measures how far a body reaches from its initial point.

Displacement Definition

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It is the shortest distance between the initial point and the final point. It prefers straight line path over curved path and is a Vector quantity. It is given by $\Delta$ S. It SI unit is meters (m).

Displacement Formula

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The displacement is calculated where ever body undergoes motion so there is no single formula for motion but are few significant formulas
S = v t
or
S = ut + $\frac{1}{2}$ at2
Where u and v are initial and final velocities, a is the acceleration and t is the time taken.

Example of Displacement

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A school boy walks from point A. He moves 3 km east and reaches point B, 4 km in the north to reach point C. Here actual path traveled is in total 7 km. But if we measure how far he is from initial point A. It will just 5m.
Example of Displacement
Displacement S = $\sqrt{AB^2 + BC^2}$ = $\sqrt{3^2 + 4^2}$ = 5m

A man starts from his home from point A. He moves 3 km north and reaches point B, 5 km in the west to reach point C. Then 3 km in the south to reach point D and finally 3 km to east and comes the same initial point A. Here path traversed by him is 3 + 5 + 3 + 5 = 16 km. But the man is still at the same point where he started hence his displacement is zero.
Displacement and Distance
Displacement = 0

Resultant Displacement

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The resultant term itself states its a summing up or totaling. The Resultant displacement is the sum total of the displacement of all the paths chosen. Lets say that a man moves in any n number of path to reach his final destiny. The resultant displacement is the sum total of the displacements of all these paths from the initial point.
Resultant Displacement = Shortest distance for all the paths chosen from start to end point.

Is Displacement a Vector?

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Its often being confused by many that since distance is scalar displacement might also be so. But you could see that distance traveled might be in any direction what actually is seen is the actual path chosen whereas the displacement is the path chosen in the specific direction of shorter path from the initial point to the end point.
Hence Displacement is a vector

Distance Vs Displacement

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Lets see the some difference between distance and displacement:


Distance
Displacement
1
It is the actual path taken It is the shortest distance from the initial point to the final point.
2
It is a scalar quantity It is a vector quantity
3 It will always be positive It can be positive, negative or zero
4
It can never be less than displacement It will be less than or equal to distance traveled

Is Displacement Negative?

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Yes it can be a negative quantity. You know that Displacement always takes place in a specific direction and hence called as vector quantity. A negative displacement does not mean that the body speed has decreased but specifies that the displacement takes place in opposite direction to given direction.

The positive displacement is from A to B is + 5m whereas the negative displacement from B to A is - 5m.