Kinematics (1D) II- Distance and Displacement

Distance

The total length covered or the Individual sum of all the lengths that a body covers when it is in motion is called distance. It is a scalar quantity (has magnitude but no directions).  Distance is always positive. The reason behind this is that distance is a scalar quantity. The directions are not considered so there is no chance that -ve sign or convention can be taken to determine distance which means every value that you consider here will be positive.

Total distance = the sum of all the individual length (calculated in some units) of the paths covered by body. (One individual length is just one unit of length. For example if you are measuring in meters, one individual length is 1 meter). Its standard unit is m (meter). Distance is a particular parameter which is used to determine the position of an object with respect to another object.

Example- the man is 500 meters away from the building which is located at the east.

Other units of displacement are centimetres, nanometers, Planck lengths, light years, Astronomical units etc.

(read the last two topics for deeper understanding of distance)

Displacement

Displacement is the shortest possible distance between two points. In a plane or 2D surface, the shortest distance between two points is a straight line. Displacement is a vector quantity (magnitude and direction). Therefore, displacement can be negative and zero as well. When will it be negative? This can be explained using the number line below.

Let the original position of an object be 0. When the particle moves from 0 to 3, it has a displacement of 3 units. When it moves from 0 to -2, it has a displacement of -2 units.

Total displacement is found by subtracting the value of final position from the value of initial position.

for example as discussed earlier, the displacement when a particle moves from 0 to -2 is calculated like this> ( -2) – (0) = -2.

The various units of displacement are the same as the various units of distance.

Relation between distance and displacement

The distance is same as displacement when a particle moves in the same direction on a straight path. distance is path dependent whereas displacement is not. look at the figure below-

The distance is equal to the length of the actual path taken by the object. But, the Displacement is just depends on the difference between the starting and ending points. Read the next part for more understanding.

Displacement can be zero

Imagine the number line once again. Let the object travel from 0 to 3 and then back to 0. Both the initial and final points are same (=0). the total distance is path dependent. distance covered from 0 to 3 is three units and from 3 to 0 is again 3 units. The total distance traveled is 6 units. The displacement is 0 (0-0=0).

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