Physics · Motion In A Straight Line · NEET
Yes. Distance is a scalar that only adds up (it never shrinks), so any real motion gives a positive distance. Displacement is a vector: start position to end position. If the object ends exactly where it started, the two positions are the same, so displacement = 0 even though the distance is large. Example: run one full lap of a 400 m track. Distance = 400 m, displacement = 0.
When you move forward, distance adds a positive number and displacement also grows. But when you turn back, distance still adds (it never goes negative), while displacement now decreases because you are getting closer to the start again. The forward and backward parts of displacement cancel, but the path lengths cannot cancel. That mismatch is exactly why displacement can be zero while distance is not.
No, turning around alone does not make displacement zero. Displacement is zero only if the final position equals the initial position. A particle can go 8 m forward, turn, come back 3 m and stop: distance = 11 m, displacement = +5 m. It becomes zero only when it comes back the full 8 m to its start.
Average velocity = displacement / time and average speed = distance / time. When displacement is zero but distance is not (a round trip), average velocity = 0 but average speed is a real positive number. This is a favourite NEET setup: they give you position s(t), you find where it reverses, and if it returns to the start the average velocity is 0 while average speed is not.
A 100 m straight sprint has the start and finish at different points on one straight line without reversing, so distance = displacement = 100 m. A looped course brings you back near or exactly to the start, so the straight gap (displacement) is small or zero even though the path length (distance) is huge. Direction changes and returning are what split the two.
A particle moves along a straight line with position s(t) = alpha*t^2 - beta*t + gamma, where alpha = 1 m/s^2, beta = 6 m/s, gamma = 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.
No. Distance is always greater than or equal to the magnitude of displacement. They are equal only for motion in a single straight line without any reversal. The moment the object changes direction or curves, distance becomes larger than displacement.
Only for one complete revolution (or a whole number of revolutions), because you end where you started. For half a circle, displacement equals the diameter, and distance equals half the circumference (pi*r), so they are not equal.
For one complete circle of radius r, distance = 2*pi*r (the circumference) and displacement = 0. The ratio is undefined (division by zero). For a half circle, distance = pi*r and displacement = 2r, giving ratio pi/2.
No. Zero displacement only means the object came back to its starting position. It can have travelled a long path (large distance) and had non-zero speed the whole time. Zero displacement over an interval never means zero motion.
Because it separates students who memorise formulas from those who understand vectors. A single sign error or picking distance instead of displacement flips the answer. Nearly every average velocity vs average speed question is built on this one idea.
