Hey mate! Free points! How can we find the magnitude of displacement?
The Correct Answer and Explanation is:
Correct Answer:
The magnitude of displacement is the straight-line distance between the initial position and the final position of an object, along with the direction. To calculate it, use the distance formula derived from the Pythagorean theorem:Displacement=(x2−x1)2+(y2−y1)2\text{Displacement} = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}Displacement=(x2−x1)2+(y2−y1)2
Where:
- (x1,y1)(x_1, y_1)(x1,y1) is the initial position
- (x2,y2)(x_2, y_2)(x2,y2) is the final position
Explanation:
Displacement is a fundamental concept in physics and mathematics. It refers to how far out of place an object is. In simple terms, it is the object’s overall change in position. While distance measures the total path traveled, displacement focuses only on the starting and ending points, ignoring the route taken in between.
To understand the magnitude of displacement better, imagine walking from one corner of a football field to the diagonally opposite corner. Even though you might take several turns and cover a large distance, your displacement is simply the length of the diagonal between the two corners. That straight-line distance is your displacement.
Now let us say an object moves from point A with coordinates (2, 3) to point B at (7, 11). The magnitude of displacement can be found using the formula:(7−2)2+(11−3)2=25+64=89≈9.43 units\sqrt{(7 – 2)^2 + (11 – 3)^2} = \sqrt{25 + 64} = \sqrt{89} \approx 9.43 \text{ units}(7−2)2+(11−3)2=25+64=89≈9.43 units
This value tells us how far the object is from where it started, regardless of the path it followed.
Displacement can also be applied in one dimension. For example, if a car drives 40 kilometers east and then 30 kilometers west, the displacement is not 70 kilometers. Instead, the net displacement is 10 kilometers to the east.
This concept is essential in areas like navigation, physics, and engineering. It helps describe motion accurately and efficiently, particularly in calculations involving velocity and acceleration.
