Physics · Motion In A Plane · NEET
Pick any fixed point as the origin O. Draw a straight arrow from O to the particle at point P. That arrow OP is the position vector, written r. Its length is the distance of the particle from O, and its direction is the direction of P as seen from O. In 2D you write it as r = x i + y j, where x and y are the coordinates of the particle.
A position vector is measured from the origin at ONE instant. A displacement vector is measured between TWO instants: it is the straight arrow from the first position P (at time t) to the second position P' (at time t'). In symbols, displacement = r' - r = (x'-x) i + (y'-y) j. So displacement is a change in position, not a position itself.
Displacement is 'change', and in physics every change is final value minus initial value (like v - u for velocity). The arrow must start at where you were and end at where you are now. If you reverse it (initial minus final) you get a vector of the same length pointing backwards, which is wrong.
No. Distance is a scalar equal to the actual path length, which is always positive and depends on the path. Displacement is a vector equal to the straight-line arrow from start to finish. The magnitude of displacement is always less than or equal to the distance. They are equal only when the motion is along a straight line without turning back.
Yes. The position vector depends on where you place the origin O, because it is drawn from O. But the displacement vector does NOT depend on the origin: r' - r cancels the origin out, so shifting the origin leaves displacement unchanged. This is why displacement is the 'physically real' quantity for motion in a plane.
Yes. If the particle returns to its starting point (for example one full circle, or going and coming back), the final and initial positions are the same, so r' - r = 0. Displacement is zero, but the distance travelled is not zero. NEET loves this trap in circular motion.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
It is a vector. It has both magnitude (distance from origin) and direction (the direction of the particle as seen from O).
If the particle goes from (x1, y1) to (x2, y2), then displacement = r2 - r1 = (x2 - x1) i + (y2 - y1) j. Its magnitude is sqrt((x2-x1)^2 + (y2-y1)^2).
Because velocity and acceleration in a plane are built from the change in position vector. Displacement is the vector quantity that feeds directly into v = dr/dt, so it links straight to the rest of Motion in a Plane.
No, never. The straight line is the shortest path between two points, so |displacement| <= distance always. They are equal only for straight-line motion in one direction.
As a vector it has a direction rather than a plain sign. In one dimension along a line, this direction shows up as a plus or minus sign depending on which way the particle ends up relative to the start.
