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Distance and Displacement

In Physics, we have to be able to describe the motion (or in simple words, movement) of the objects where object might be as small as an ant or as big as an Plane. One of the important way to describe the motion is "how far the object moved?". This parameter can be described by either of these two -

  1. Distance
  2. Displacement
So, what is distance and what is displacement?
Distance is the length of the path covered in the of motion of a object while Displacement is the length of the straight line between the initial position of the object before movement (or motion) and final position of the object after movement with the direction.

Simple Definition :
Distance - Distance is the total length of path traversed by the moving body without worrying about direction.
Displacement - Displacement is the line segment with direction between initial and final position of a moving body.So, distance is a scalar (only magnitude but no direction), on the other hand, displacement is vector (magnitude with direction). So, displacement has a direction but which direction? Easy.. direction will be mentioned with the answer.

Distance and Displacement

Like in the above diagram, movement happened from A to C through B (A to B and then B to C). In this case, Distance is be 7 meters (length of the path covered = sum of length AB and length of BC). Although, displacement is 5 meters in the direction of AC (Length of line segment between initial position, A and final position, C = Length of the line segment AC).

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Difference between Distance and Displacement

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Distance Displacement
It is the actual length of the path covered by a moving object. It is the shortest distance between the initial position and the final position of the moving object.
It is a scalar quantity (only magnitude). It is a vector quantity (magnitude and direction).

For a particular movement, the magnitude of displacement can be lesser or equal to the magnitude of the distance. For the movement in straight line, the magnitude of displacement will be equal to magnitude otherwise, it will be lesser.

For a movement where the object moves and comes back to the original position, the magnitude of displacement will be zero but magnitude of distance will be greater than zero. In the case of body not moving at all, both the magnitudes (distance and displacement) will be zero. Like in this case, where bus goes from A to B and comes back from B to A. Distance traveled is twice the length of AB, although Displacement is zero.
Zero Displacement

Can Displacement be Negative?

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Yes, displacement can be negative. If the movement in in the opposite of reference direction, the displacement magnitude will be negative.
A displacement of 10 miles in East direction is same as displacement of -10 miles in West direction since East and West are exactly opposite.

Can Distance be Negative?

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No, distance cannot be negative. Since the distance is the length of the path covered irrespective of the direction, it cannot be negative.

Speed and Velocity

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Speed and Velocity are related to distance and displacement respectively. Distance per unit time is speed, however displacement per unit time is velocity. So, speed is scalar (magnitude but no direction) similar to distance, however, velocity is vector (magnitude with direction) similar to displacement.
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