Physics 5054/12 — May/June 2017

Walkthrough

We are asked to identify the quantity that is a scalar. A scalar quantity is described completely by its magnitude (size) alone, with no direction needed.

Examine each option:

• A: displacement of 40 m — displacement is a vector because it specifies how far and in which direction an object has moved. Even if no direction is written in the option, displacement is still a vector quantity.
• B: a time of 4.0 s — time has only a magnitude. There is no direction associated with time, so it is a scalar.
• C: a velocity of 20 m/s — velocity is speed in a particular direction, so it is a vector.
• D: an acceleration of 5.0 m/s² — acceleration is the rate of change of velocity and therefore also has a direction, so it is a vector.

Therefore the scalar quantity is time.

Key Takeaways

• Scalars have magnitude only: time, mass, distance, speed, energy, temperature.
• Vectors have magnitude and direction: displacement, velocity, acceleration, force, momentum.
• The units alone do not tell you whether a quantity is a scalar or a vector; you must think about whether direction is part of the quantity.

Common Mistakes

• Thinking displacement is a scalar because it is sometimes confused with distance. Displacement is always a vector.
• Thinking velocity is a scalar because it has a speed value in m/s. Velocity always includes direction.
• Forgetting that acceleration is a vector; acceleration can be positive or negative depending on direction, which shows it has direction.

Things to Be Careful About

• A quantity such as speed is scalar, but velocity is its vector counterpart. Watch the exact word used in the question.
• The absence of an arrow or direction symbol in the printed option does not change whether the quantity is fundamentally a vector.
• Time is one of the clearest scalar quantities in O Level Physics — it never has a direction.