Understanding the Length of Path Travelled in Physics and Mathematics: Calculation Methods and Concepts

The length of path travelled.

The length of path travelled is a term commonly used in physics and mathematics to describe the distance covered by an object or a person as they move from one point to another

The length of path travelled is a term commonly used in physics and mathematics to describe the distance covered by an object or a person as they move from one point to another. It is a scalar quantity that represents the total length of the path along which an object has moved.

To understand the concept of length of path travelled, let’s consider an example. Suppose you start at point A and walk in a straight line to point B. Along the way, you may encounter obstacles or make slight deviations from the straight path. The length of path travelled would be the total distance covered by your movement, taking into account any detours or changes in direction.

In mathematics, we can calculate the length of path travelled using various methods depending on the complexity of the path. For a straight line path, the distance can be found using the distance formula:

Distance = √[(x₂ – x₁)² + (y₂ – y₁)²]

Here, (x₁, y₁) represent the coordinates of the starting point, and (x₂, y₂) represent the coordinates of the ending point.

For a more complex path, such as a curve or a curved line, we can use calculus concepts such as integration to find the length. This involves breaking down the path into infinitesimally small segments and summing the lengths of these segments.

It is important to note that the length of path travelled is different from displacement. Displacement refers to the shortest straight-line distance between the starting and ending points, regardless of any detours or changes in direction. On the other hand, the length of path travelled takes into account the actual distance covered, including any changes in direction or deviations from a straight line.

In summary, the length of path travelled is a measurement of the total distance covered by an object or a person along a given path. It considers all changes in direction, detours, and deviations from a straight line, and can be calculated using different methods depending on the complexity of the path.

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