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| Distance and Displacement |
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| The distance between terminus A and terminus B is 150 km. A bus travels from terminus A to terminus B. The distance covered by the bus is 150 km. The bus travelling on the same route, returns from terminus B to the terminus A. Thus the total distance covered by the bus during the trip from A to B and then from B to A is 150 km + 150 km = 300 km. |
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| A Bus Moving from A to B and Again from B to A |
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| The distance covered by a moving object is the actual length of the path followed by the object. |
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| Distance is a scalar quantity. SI unit of distance is metre. |
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| The position of the bus changed when it moved from the terminus A to terminus B. There is a displacement of 150 km from A to B. The displacement by the return trip is also 150 km . |
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| Displacement is the shortest distance covered by a moving object from the point of reference (initial position of the body), in a specified direction. |
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| Note: |
But the displacement when the bus moves from A  B and then from B  A is zero. SI unit of displacement is metre. |
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| Displacement is a vector, i.e., the displacement is given by a number with proper units and direction. |
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| To drive home the difference between displacement and distance let us consider a few more examples. |
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| Suppose a person moves 3 metres from A to B and 4 metres from B to C as shown in the figure. The total distance travelled by him is 7 metres. But is he actually 7 metres from his initial position? No, he is only 5 metres 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. |
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| Distance and Displacement |
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| In this example we can make use of the Pythagoras theorem to determine the displacement. |
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| 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 and final positions of the object. Then the displacement of the object = xf
- xi |
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| Suppose the object is moving from +1 to +4, |
| then displacement = xf - xi |
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= +4 - (+1) |
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| = +3 |
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| Displacement: Case1 |
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| If the object is moving from -3 to -1, |
| then displacement = xf - xi |
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| = -1 - (-3) |
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| = 2 |
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| Displacement: Case 2 |
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| If the object is moving from +4 to +2, |
| then displacement = xf - xi |
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| = +2 - (+4) |
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| = -2 |
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| Displacement: Case 3 |
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| If the object follows the path as shown in the figure then the final position and the initial position are the same i.e., the displacement is zero. |
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| Displacement: Case 4 |
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| 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. When a moving object comes back to the original position the displacement is said to be zero. |
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| Imagine an athlete running along a circular track of radius r in a clockwise direction starting from A. |
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| A Circular Track of Radius r |
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| What is the distance covered by the athelete when he reaches the point B? |
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The distance covered by the athlete when he reaches the point B is  |
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| Displacement = AB = 2r = Diameter of the circle (the shortest distance between the initial and final positions). |
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| Suppose the athlete reaches the initial point A, then the distance covered is equal to the circumference of the circular track i.e., 2pr. But the displacement is zero as the initial and final positions of the athlete are the same. |
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