Distance, and, Displacement, Distance and Displacement Distance - The length of the actual path travels by an object during moti...
Distance, and, Displacement,
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| Distance and Displacement |
Distance- The length of the actual path travels by an object during motion in a given interval of time is called distance travelled by that object.
from the above figure the distance is total path traveled by biker to reach factory from home which is 200 meter.
Distance is scalar quantity. So Its value can never be zero or negative, during the motion of an object.
Displacement- The displacement of an object in a given interval of time is define as the change its position of the object along a particular direction during that time and is given by the vector drawn from the initial position to its final position.
from the above figure displacement is the straight and shortest distance/path between home and factory.
Note- *Displacement May be zero or negative
*Displacement equal or less than distance but not greater than distance.
Some Numerical Examples
Example 1: An object moves from point A to point B to point C, then back to point B and then to point C along the line shown in the figure below.
a) Find the distance covered by the moving object.
b) Find the magnitude and direction of the displacement of the object.
Solution :-
a) Distance = AB + BC + CB + BC = 5 + 4 + 4 + 4 = 17 km
b) The magnitude of the Displacement is equal to the Distance between the final point C and the initial point A = AC = 9 km
The direction of the Displacement is the direction of the ray AB.
Example 2: An object moves along the grid through the points A, B, C, D, E, and F as shown below.
a) Find the Distance covered by the moving object.
b) Find the magnitude of the Displacement of the object
Solution :-
a) Distance = AB + BC + CD + DE + EF = 3 + 1 + 1.5 + 0.5 + 0.5 = 6.5 km
b) Initial point is A and the final point is F, hence the magnitude of the displacement is equal to the distance AF which is calculated by applying Pythagoras's theorem to the triangle AHF as shown in the figure below
from the above figure displacement is the straight and shortest distance/path between home and factory.
Note- *Displacement May be zero or negative
*Displacement equal or less than distance but not greater than distance.
Some Numerical Examples
Example 1: An object moves from point A to point B to point C, then back to point B and then to point C along the line shown in the figure below.
a) Find the distance covered by the moving object.
b) Find the magnitude and direction of the displacement of the object.
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| Distance and Displacement |
Solution :-
a) Distance = AB + BC + CB + BC = 5 + 4 + 4 + 4 = 17 km
b) The magnitude of the Displacement is equal to the Distance between the final point C and the initial point A = AC = 9 km
The direction of the Displacement is the direction of the ray AB.
Example 2: An object moves along the grid through the points A, B, C, D, E, and F as shown below.
a) Find the Distance covered by the moving object.
b) Find the magnitude of the Displacement of the object
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| Distance and Displacement |
a) Distance = AB + BC + CD + DE + EF = 3 + 1 + 1.5 + 0.5 + 0.5 = 6.5 km
b) Initial point is A and the final point is F, hence the magnitude of the displacement is equal to the distance AF which is calculated by applying Pythagoras's theorem to the triangle AHF as shown in the figure below
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| distance and displacement |
AF2 = AH2 + HF2 = (0.5*4)2 + (0.5*3)2 = 4 + 2.25 = 6.25
magnitude of displacement = AF = 2.5 km
magnitude of displacement = AF = 2.5 km
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