Distance, Displacement, Speed & Velocity

• Distance — total path length travelled (scalar, always positive).
• Displacement — shortest straight-line change in position from start to finish (vector; can be zero, positive, or negative).
• Speed — distance per unit time; velocity — displacement per unit time (includes direction).
• Uniform motion — equal distances in equal time intervals; non-uniform — unequal distances in equal intervals.
• SI units: metre (m), second (s), m/s for speed/velocity.

1. Distance (s) — scalar; path dependent; e.g. one full lap of 400 m track → distance = 400 m.
2. Displacement (Δx) — vector; depends only on initial and final positions; one lap → displacement = 0.
3. Average speed = total distance / total time; average velocity = total displacement / total time.
4. Instantaneous speed — speed at a particular instant (speedometer reading).
5. Uniform vs non-uniform — car at steady 60 km/h (uniform); city traffic (non-uniform).
6. Diagram (text) — A→B→C along L-shaped path: distance = AB + BC; displacement = straight line A to C.
7. NCERT Ch. 8 — odometer measures distance; straight-line map distance gives displacement magnitude.
8. Real world — flight Delhi→Mumbai: path length (distance) > straight-line separation (displacement).

A student walks 40 m east, then 30 m north. Find distance and displacement magnitude.

Step 1 — Distance = 40 + 30 = 70 m (total path).
Step 2 — Displacement forms right triangle: |Δ| = √(40² + 30²) = √(1600 + 900) = √2500 = 50 m.
Step 3 — Direction: tan θ = 30/40 → θ ≈ 37° north of east.
Step 4 — Average speed for 70 s journey: 70/70 = 1 m/s; avg velocity magnitude: 50/70 ≈ 0.71 m/s.
Conclusion: distance ≥ |displacement|; equal only for straight-line motion in one direction.

• Using distance and displacement interchangeably (return trip → distance > 0, displacement = 0).
• Misconception: speed and velocity are always equal (only for straight-line motion without turning back).
• Forgetting direction for velocity (velocity is a vector).
• Adding speeds directly when directions differ (need vector addition).
• Confusing km/h with m/s without conversion (× 5/18 or × 18/5).

• Define distance and displacement with one example each.
• A car travels 100 km north and returns 100 km south. Find distance and displacement.
• Convert 72 km/h to m/s.
• When is average speed equal to the magnitude of average velocity?

Open the Practice tab for graded questions on Distance, Displacement, Speed & Velocity.