Distance and Displacement

Distance:

1. Total length of the path traveled.
2. Scalar quantity (no direction).
3. Measured in units of length (meters, kilometers, etc.).
4. Always positive (or zero).

Example: Traveling from point A to point B and back to point A, the distance covered is the total length of the journey (e.g., 20 km + 20 km = 40 km).

Displacement:

1. Change in position from initial to final point.
2. Vector quantity (has direction).
3. Measured in units of length (meters, kilometers, etc.).
4. Can be positive, negative, or zero.

Key differences:

1. Direction: it has direction, distance doesn’t.
2. Magnitude: it can be less than or equal to distance.
3. Calculation: Distance = Σ (all distances traveled), Displacement = final position – initial position.

Formulas:

1. Distance = Speed × Time.
2. Displacement = Δx = xf – xi (final position – initial position).

Examples:

1. A car travels 100 km north and then 50 km south.
2. Distance = 150 km, Displacement = 50 km north.
3. A ball thrown upwards returns to the thrower’s hand. Distance = 20 m (up + down), Displacement = 0 m.

Real-world applications:

1. Navigation (GPS)
2. Physics and engineering
3. Sports (track and field, racing)
4. Transportation (route planning)