Q.Classify the following measures as scalars and vectors.

Rule. A scalar has magnitude only; a vector has magnitude and direction. Force is a vector by its nature, even when its direction is not written out.

• (i) $5$ seconds — time → scalar
• (ii) $1000\ \text{cm}^3$ — volume → scalar
• (iii) $10$ Newton — force → vector
• (iv) $30\ \text{km/hr}$ — speed → scalar …

The test

Ask one question of each quantity: does it need a direction to be complete? If yes, it is a vector; if a number with its unit says everything, it is a scalar. Note that a quantity like force is a vector by its physical nature — it always acts in some direction — even if that direction is not spelled out in the problem.

Item by item

1. $5$ seconds — time carries no direction. Scalar.
2. $1000\ \text{cm}^3$ — volume is an amount of space, direction-free. Scalar.
3. $10$ Newton — the newton is the unit of force, and force is a vector (it has a line of action and a sense). So this measures a vector quantity. Vector.
4. $30\ \text{km/hr}$ — this is a speed (how fast, no direction). Had it said "towards north", it would be velocity. As written, scalar. …

Method: Classifying a quantity as scalar or vector

Apply this test to any physical measure to decide whether it is a scalar (magnitude only) or a vector (magnitude and direction).

Steps

Step 1: Ask "does it need a direction to be fully specified?"

If a number-with-unit says everything (time, volume, density, mass, speed), it is a scalar. If a direction is essential to its meaning (displacement, velocity, force), it is a vector.

Step 2: Watch for quantities that are vectors by their physical nature. …

Common Mistakes

Mistake 1: Calling $10$ N a scalar because no direction is written.

Why it's wrong: force is a vector by its physical nature — it always acts along a line — even when the direction is not spelled out in the numbers. Correct approach: classify force, velocity, and displacement as vectors regardless of whether a direction is stated.

Mistake 2: Treating any rate (km/hr, m/s) as automatically a vector. …