# Distance and Displacement

## Difference between distance and displacement

### Example 1

Suppose a bus starting from a terminus A travels 15000 m to reach terminus B. Then the distance covered by the bus is 15000 m. Now if the bus returns to the terminus A, then what is the distance covered by the bus during the return trip? The distance covered is 15000 m. But the total distance covered by the bus during the trip from A to B and than back to A from B is 15000 m + 15000 m = 30000 m.

A bus moving from A to B and again from B to A

Thus, the distance covered by a moving object is the actual length of the path followed by the object.

Distance is a scalar quantity. SI unit of distance is meter.

Now let us find out whether the position of the bus has changed when it is moving from the terminus A to terminus B. Yes, the position has changed, i.e., there is a displacement of 15000 m from A to B. What is the displacement of the bus during the return trip? The displacement is again 15000 m but from B to A.

Thus, displacement is the shortest distance covered by a moving object from the point of reference (initial position of the body), in a specified direction.

But the displacement when the bus moves from A → B and then from B → A is zero. SI unit of displacement in meter.

Displacement is a vector, i.e., the displacement is given by a number with proper units and direction.

To drive home the difference between displacement and distance let us consider a few more examples.

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### Example 2

Suppose a person moves 3 meters from A to B and 4 meters from B to C as shown in the figure. The total distance traveled by him is 7 meters. But is he actually 7 meters from his initial position? No, he is only 5 meters away from his initial position i.e., he is displaced only by 5 m, which is the shortest distance between his initial position and final position.

Now let us consider an object changing its position, with respect to a fixed point called the origin 0. xi and xf are the initial position and final position of the object. Then the displacement of the object = xf – xi.

#### Case 1

Suppose the object is moving from +1 to +4

then displacement = xf – xi

= +4 – (+1)

= +3

#### Case 2

If the object follows the path as shown in the figure then the final position and the initial position is the same i.e., the displacement is zero.

From the above examples, we can conclude that the displacement of a body is positive if its final position lies on the right side of the initial position and negative if its final position is on the left side of its initial position. Whenever a moving object comes back to the original position then the displacement is zero.

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