Physics · Motion In A Straight Line · NEET
| Type of quantity | Scalar (only magnitude) | Vector (magnitude + direction) |
| Depends on path? | Yes, uses the whole actual path | No, uses only start and end positions |
| Sign | Always positive (or zero if no motion) | Can be positive, negative or zero |
| Formula | Sum of all path lengths covered | x(final) - x(initial) |
| When they are equal | Same value only for straight-line, no-reversal motion | Otherwise |displacement| < distance |
Distance is always greater than OR equal to the magnitude of displacement. It is never smaller. They are equal only when the motion is in a straight line without any turning back or reversing. The moment the path curves or the object retraces even a little, distance becomes larger than displacement. So the safe rule is: distance >= |displacement|, always.
Yes, when an object moves along a straight line in one single direction and never reverses. For example, a car going 100 m due east in a straight road has distance = 100 m and displacement = 100 m east. Both have the same magnitude here. As soon as it turns or comes back, they stop being equal.
Displacement tells you both how far the position changed AND in which direction (east, up, +x). Direction is essential to it, so it is a vector. Distance only tells you the total path length, a plain number of metres with no direction attached, so it is a scalar. In NEET this decides which rules apply: vectors add head-to-tail, scalars just add up.
Yes. In one dimension we use a sign convention (+x to the right, -x to the left). If the final position is on the negative side of the start, displacement is negative, like -5 m, meaning 5 m in the -x direction. Distance is a total path length, so it is never negative and never zero unless the object never moved.
Yes. Displacement = final position minus initial position, that is x(final) - x(initial). This is exactly the change in position. It does not care about the path taken in between, only the two endpoints. Distance, in contrast, does depend on the whole path.
A particle moves along a straight line with position s(t) = a t^2 - b t + c, where a = 1 m/s^2, b = 6 m/s, c = 5 m. The average speed of the particle (in m/s) from t = 0 to t = 6 s is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Distance is the total path length (scalar, always positive); displacement is the shortest straight-line change in position with direction (vector, can be positive, negative or zero).
No. The magnitude of displacement can at most equal distance (straight-line motion), never exceed it, because the straight line is the shortest route between two points.
Both are measured in metres (m), because both describe length. The difference is that displacement also carries a direction.
Yes. Distance depends fully on the actual path. Displacement does not; it only depends on the start and end positions.
Distance equals the full circumference of the track, but displacement is zero because the runner ends exactly where they started.
