Understanding Net Displacement: Calculating the Overall Change in Position of an Object

net displacement

Net displacement refers to the overall change in position of an object

Net displacement refers to the overall change in position of an object. It is a vector quantity, which means it has both magnitude (size) and direction. To calculate the net displacement, you need to consider both the distance traveled and the direction traveled.

If an object moves in a straight line, the net displacement is equal to the distance traveled in that direction. For example, if an object moves 10 meters to the east, the net displacement is 10 meters east.

However, if an object moves in more than one direction or changes direction during its motion, the net displacement is determined by the vector sum of its individual displacements. To calculate the net displacement in such cases, you can use vector addition.

Let’s say an object moves 5 meters to the east and then 3 meters to the north. To find the net displacement, you would draw a vector representing each displacement and add them together.

If you construct a right-angled triangle with the 5-meter east displacement as the base and the 3-meter north displacement as the height, you can use the Pythagorean theorem to find the hypotenuse, which represents the net displacement.

The Pythagorean theorem states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):

c^2 = a^2 + b^2

In this case, a = 5 meters and b = 3 meters. Plugging these values into the equation:

c^2 = 5^2 + 3^2
c^2 = 25 + 9
c^2 = 34

Taking the square root of both sides, we find that c ≈ √34 ≈ 5.83 meters.

Therefore, the net displacement of the object is approximately 5.83 meters, in a direction that is a combination of east and north. This can be represented as a vector with a magnitude of 5.83 meters and an angle relative to the eastward direction, which can be determined using trigonometry.

Remember to pay attention to the signs of the displacements as positive or negative, depending on the chosen coordinate system, when performing vector addition to find the net displacement.

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