Scalars and Vectors

A scalar quantity has magnitude (size) only — it does not have a direction. A vector quantity has both magnitude and direction.

Velocity requires a direction (e.g. 60 km/h north). Weight is a gravitational force acting downward — direction is required. Acceleration has a direction (e.g. 9.8 m/s² downward).

Temperature (e.g. 25°C) is fully described by a number and a unit. You do not say temperature is '25°C downward' — it has no direction. Temperature is therefore a scalar.

We need to find the quantity that has magnitude only (no direction needed).

Velocity is the rate of change of displacement and requires a direction (e.g. 60 km/h east). It is a vector. Eliminate velocity.

Weight is a gravitational force that acts downward — direction is essential. It is a vector quantity. Eliminate weight.

Acceleration describes how velocity changes, and it always has a direction (e.g. 9.8 m/s² downward). It is a vector. Eliminate acceleration.

Temperature (e.g. −60°C) is fully described by a number and a unit. No direction is needed, so it is a scalar. This is the correct answer.

Distance is the total length of path travelled (scalar — always add path lengths). Displacement is the straight-line distance from start to finish, with direction (vector).

The dog runs 40 m east, then 40 m west. Total distance = $40+40=\text{80 m}$. Distance always adds regardless of direction.

The dog starts at point A and ends at point A. The straight-line distance from start to finish is zero. Displacement = 0 m.

Distance = 80 m, Displacement = 0 m. This is a classic example showing that displacement can be zero even when significant distance has been covered.

We need both the distance (total path length) and displacement (straight-line from start to finish) for a dog that returns to its starting point.

The displacement cannot be 80 m east because the dog ends up where it started, not 80 m east of the start. Eliminate this option.

Distance cannot be 0 m — the dog physically ran 80 m in total. Distance is the total path length and is never zero unless the object didn't move. Eliminate this option.

Distance = 40 m is incorrect (the dog ran 40 m east AND 40 m west = 80 m total). The displacement is also not 40 m west. Eliminate this option.

Distance = 80 m (total path: $40+40$) and Displacement = 0 m (the dog returns to start). This is the correct answer.