How to Find Displacement in Standard American English
Displacement is the distance an object moves from its original position. It is a vector quantity, which means it has both magnitude and direction. The magnitude of displacement is the length of the straight line from the object’s original position to its final position. The direction of displacement is the angle between the straight line and a reference direction.
To find the displacement of an object, you need to know its original position and its final position. Once you have this information, you can use the following formula to calculate the displacement:
displacement = final position - original positionFor example, if an object moves from a position of (2, 3) to a position of (5, 7), its displacement would be:
displacement = (5, 7) - (2, 3) = (3, 4)The magnitude of the displacement would be the length of the straight line from (2, 3) to (5, 7), which is sqrt(3^2 + 4^2) = 5. The direction of the displacement would be the angle between the straight line and the x-axis, which is arctan(4/3) = 53.13 degrees.
Here are some additional examples of how to find displacement:
- If an object moves from a position of (-2, 5) to a position of (3, -1), its displacement would be:
displacement = (3, -1) - (-2, 5) = (5, -6)The magnitude of the displacement would be the length of the straight line from (-2, 5) to (3, -1), which is sqrt(5^2 + (-6)^2) = 7.81. The direction of the displacement would be the angle between the straight line and the x-axis, which is arctan(-6/5) = -48.59 degrees.
- If an object moves from a position of (0, 0) to a position of (5, 0), its displacement would be:
displacement = (5, 0) - (0, 0) = (5, 0)The magnitude of the displacement would be the length of the straight line from (0, 0) to (5, 0), which is 5. The direction of the displacement would be 0 degrees, since the object moved along the x-axis.
- If an object moves from a position of (0, 0) to a position of (0, 5), its displacement would be:
displacement = (0, 5) - (0, 0) = (0, 5)The magnitude of the displacement would be the length of the straight line from (0, 0) to (0, 5), which is 5. The direction of the displacement would be 90 degrees, since the object moved along the y-axis.
FAQ
What is the difference between displacement and distance?
Distance is the total length of the path an object travels, while displacement is the net change in the object’s position. For example, if an object moves from a position of (2, 3) to a position of (5, 7), its distance traveled would be the length of the path it took to get there, which is sqrt((5-2)^2 + (7-3)^2) = 5.83. Its displacement, on the other hand, would be (5, 7) – (2, 3) = (3, 4), since this is the net change in its position.
Can displacement be negative?
Yes, displacement can be negative. A negative displacement indicates that the object has moved in the opposite direction of the reference direction. For example, if an object moves from a position of (2, 3) to a position of (-1, 0), its displacement would be (-1, 0) – (2, 3) = (-3, -3). This indicates that the object has moved 3 units to the left and 3 units down from its original position.
What are the units of displacement?
The units of displacement are the same as the units of distance. In the metric system, the units of displacement are meters. In the English system, the units of displacement are feet or inches.
How can I use displacement to solve problems?
Displacement can be used to solve a variety of problems, such as:
- Finding the distance an object has traveled
- Finding the direction an object has moved
- Predicting the future position of an object
For example, if you know the displacement of an object and its initial position, you can use the following formula to find its final position:
final position = original position + displacementSimilarly, if you know the displacement of an object and its final position, you can use the following formula to find its original position:
original position = final position - displacement
