avståndsvectorn

An avståndsvectorn, or displacement vector in English, is a fundamental concept in physics and mathematics used to describe the change in position of an object. It is a vector quantity, meaning it has both magnitude and direction. The magnitude of the avståndsvectorn represents the straight-line distance between the initial and final positions, while its direction points from the starting point to the ending point.

To calculate an avståndsvectorn, one subtracts the initial position vector from the final position vector. If an object starts at point A with position vector r_A and moves to point B with position vector r_B, the avståndsvectorn from A to B, often denoted as d or Δr, is given by d = r_B - r_A. In a one-dimensional case, this simplifies to the difference between the final and initial coordinates. In two or three dimensions, the subtraction is performed component-wise.

The avståndsvectorn is distinct from the distance traveled, which is a scalar quantity representing the total path length covered by an object. For instance, if an object moves in a circle and returns to its starting point, its avståndsvectorn is zero, even though the distance traveled is equal to the circumference of the circle. Understanding the avståndsvectorn is crucial for analyzing motion, calculating velocity and acceleration, and solving problems in kinematics and mechanics.