Physics
Physics
Problem
(a) Define the term position vector for a particle moving in a plane with respect to an origin O. (b) What do you understand by the displacement vector of the particle between two instants of time? (c) With the help of a neat, labelled sketch on an x–y coordinate plane, illustrate the geometric difference between position vector and displacement vector. (d) State two reasons why displacement is treated as a vector quantity whereas distance is not.Intuitive explanation
A position vector pinpoints exactly where a particle is at any moment by drawing an arrow from a fixed origin O to the particle's location—it's your GPS coordinate in vector form. Displacement, by contrast, is the straight-line arrow connecting where the particle started to where it ended between two time instants, ignoring the actual path taken. The key insight is that position tells you location, while displacement tells you change in location—and this difference matters because displacement captures direction and can cancel out (a round trip has zero displacement), whereas distance just adds up. Understanding this distinction unlocks why vectors are essential for motion: they encode both magnitude and direction, letting us describe how things actually move through space.
Intuitive explanation
A position vector pinpoints exactly where a particle is at any moment by drawing an arrow from a fixed origin O to the particle's location—it's your GPS coordinate in vector form. Displacement, by contrast, is the straight-line arrow connecting where the particle started to where it ended between two time instants, ignoring the actual path taken. The key insight is that position tells you location, while displacement tells you change in location—and this difference matters because displacement captures direction and can cancel out (a round trip has zero displacement), whereas distance just adds up. Understanding this distinction unlocks why vectors are essential for motion: they encode both magnitude and direction, letting us describe how things actually move through space.