JEE/NEET Physics · Motion in a Straight Line series · Part 1 of 6 · All parts →
- Distance = total path travelled (a scalar — just a number); displacement = straight-line change in position (a vector — number + direction)
- Speed = distance ÷ time (scalar); velocity = displacement ÷ time (vector)
- One lap of a circular track: distance = 2πr, displacement = ZERO (you end where you started)
- Average vs instantaneous: average is over a trip, instantaneous is at this exact moment (speedometer)
- In equations of motion, v always means velocity — signs (+/−) carry the direction
Walk 3 m east, then 4 m west. You walked 7 m of distance — but you are only 1 m from where you started. Both numbers are true; they answer different questions. Part 1 of the Motion in a Straight Line series — the vocabulary card every later chapter speaks.
- Distance vs displacement
- Speed vs velocity
- Average vs instantaneous
- The sign language of direction
- Solved examples
- Common mistakes
- This physics in your daily life
- Practice set
- Recap
Distance vs Displacement
Distance is what the odometer records: every metre of path, direction ignored. Displacement is what the map says: how far, and in which direction, you ended up from the start — the straight arrow from start to finish. Distance can only grow; displacement can shrink, or be zero, or point backwards.
Speed vs Velocity
Speed = distance ÷ time: a pure number. Velocity = displacement ÷ time: a number with a direction attached. Your car’s speedometer reads speed (60 km/h); your GPS computes velocity (60 km/h towards Delhi). Same trip, two reports.
Average vs Instantaneous
Average is over the whole trip: 120 km in 2 h → average speed 60 km/h, even if you stopped for tea. Instantaneous is at one frozen moment: what the speedometer says right now. When the trip has no stops and no changes, the two agree — that’s ‘uniform’ motion.
The Sign Language of Direction
In one dimension, a full compass of directions collapses to just two signs: take right as + and left as − (your choice, but stay consistent). Velocity −20 m/s isn’t ‘negative speed’ — it’s 20 m/s to the left. Signs ARE directions in 1-D physics.
| Letter | What it means (plain words) | Value / unit |
|---|---|---|
| s (or x) | position — where you are on the number line | metres (m) |
| d | distance travelled (path length, scalar) | m |
| Δx | displacement = x_final − x_start (vector) | m, sign = direction |
| v_avg | average velocity = Δx ÷ Δt | m/s (sign!) |
| speed_avg | average speed = distance ÷ time | m/s (always ≥ 0) |
Solved Examples
Distance = 400 m; displacement = 0 (back at the start).
Average speed = 400/50 = 8 m/s; average velocity = 0/50 = 0.
✔ — one lap, and velocity quietly erases the whole run.
Answer: speed 8 m/s; velocity 0
Distance = 7 m. Displacement = 3 − 4 = −1 m (1 m west of start).
Avg speed = 0.7 m/s; avg velocity = −0.1 m/s.
✔ — the minus sign is the direction west, not a ‘wrong answer’.
Answer: speed 0.7 m/s; velocity −0.1 m/s (west)
Trap: (60+30)/2 = 45 is WRONG.
Times: 30/60 = 0.5 h; 30/30 = 1 h. Total = 60 km in 1.5 h.
Average speed = 60/1.5 = 40 km/h — harmonic mean, because time — not distance — is what adds. ✔
Answer: 40 km/h
- Averaging two speeds directly. Average speed = total distance ÷ total TIME — always recompute from distances and times, never average the speeds.
- Using distance where displacement belongs. Average velocity uses Δx; a closed trip has v_avg = 0 no matter how far you walked.
- Dropping the sign. In 1-D, an unmarked 5 m/s is ambiguous — decide your + direction first and carry signs everywhere.
- Confusing the odometer with the map. Odometer = distance (only grows); map arrow = displacement (can be zero).
This Physics in Your Daily Life
- Your car has both instruments: the odometer measures distance (path travelled, only increases), the GPS arrow shows displacement (straight-line direction to your destination).
- Uber/Ola fares blend both: the fare follows the path taken (distance), but your ETA follows the displacement — a detour can triple one and leave the other unchanged.
- Treadmill stats — ‘distance 5 km, calories 300’ is distance-based; you ran in place, displacement zero, and the machine knows it.
- Fitness bands count steps (distance) but map-your-run apps draw the displacement arrow — that’s why a round-trip jog shows calories burned but ‘net movement 0 m’.
- Flight bookings show ‘distance flown’ vs ‘as-the-crow-flies’ — airlines quote path; navigation systems compute the straight arrow.
A taxi driver asks ‘how far did the meter run?’ — the passenger asks ‘how far am I from home?’. Two honest answers to two different questions. The meter never cares about direction; homesickness is purely about the straight arrow back. Physics needed both numbers, so it named them distance and displacement.
Delhi to Mumbai flight: path ≈ 1400 km (distance), straight arrow ≈ 1150 km (displacement) — airlines and crows disagree by 250 km. One lap of a 400 m track: 400 vs 0. The gap between the two numbers is a measure of how inefficient your route was.
Draw the trip as a squiggle on paper: distance is the length of squiggle you must trace with your finger; displacement is one straight ruler-line from tail to tip of the squiggle. Straighten the squiggle — distance stays, displacement is already the answer.
Practice set (answers hidden — try first)
(NEET-level) Half a circular lap of radius 7 m: distance and |displacement|:
(JEE Main-level) 60 km at 40, next 60 km at 60 km/h. Avg speed:
(NEET-level) A body ends where it started. Its average velocity is:
(Concept) The speedometer of a car reads:
(JEE Main-level) x(t) = 5t². Velocity at t = 2 s:
- distance = path (scalar); displacement = straight arrow (vector)
- speed = distance/t; velocity = displacement/t (signed)
- closed loop → displacement 0, distance ≠ 0
- average speed = total distance ÷ total time (never average speeds)
- choose + direction once, sign everything after
- 🔁 distance vs displacement
- 🔁 speed vs velocity
- 🔁 average vs instantaneous
- 🧠 Chant: ‘meter measures, arrow aims’.
- 🧠 Lap trick: one full circle — distance 2πr, displacement 0.
- 🧠 Two-speed trap: ‘time adds, so recompute — never average’.
- 🏠 Daily: odometer vs GPS arrow in your car.
- 🏠 Daily: round-trip jog burns calories at zero displacement.
Quick revision
- Distance = total path travelled (a scalar — just a number); displacement = straight-line change in position (a vector — number + direction)
- Speed = distance ÷ time (scalar); velocity = displacement ÷ time (vector)
- One lap of a circular track: distance = 2πr, displacement = ZERO (you end where you started)
- Average vs instantaneous: average is over a trip, instantaneous is at this exact moment (speedometer)
- In equations of motion, v always means velocity — signs (+/−) carry the direction
- The sign language of direction
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