NDA (II) 2022 General Ability Test · Question 102 of 150

Correct — D, speed is scalar quantity and velocity is vector quantity. Speed is the distance covered per unit time and is completely described by a number with its unit — 40 km/h and nothing more. Velocity is the displacement per unit time and is only fully stated when a direction is attached, as in 40 km/h due east. Each inherits its character from the quantity on top: distance is a scalar, displacement is a vector.

• (a)Speed and velocity both are vector quantities. — Speed carries no direction. A car going round a circular track at a steady 40 km/h has an unchanging speed but a velocity that changes at every instant — a distinction that could not exist if speed were a vector.
• (b)Speed and velocity both are scalar quantities. — Velocity does carry direction. If a body reverses its direction of motion without changing how fast it moves, the speed is unaltered but the velocity is reversed, so velocity cannot be a scalar.
• (c)Speed is vector quantity and velocity is scalar quantity. — This is the correct statement written exactly the wrong way round. It also contradicts the definitions, since speed is built on distance and velocity on displacement.

A scalar quantity is fully specified by a magnitude together with its unit. A vector quantity needs a direction as well, and it combines with other vectors by the triangle or parallelogram rule rather than by ordinary addition. Distance, speed, mass, time and energy are scalars; displacement, velocity, acceleration, force and momentum are vectors. Speed is distance divided by time and velocity is displacement divided by time, which is why the pair splits the way it does.

What the question really tests is the everyday habit of using the two words interchangeably. The cleanest way to keep them apart is the round trip — walk once around a circular field and come back to where you started, and the distance covered is the full circumference while the displacement is exactly zero, so the average speed is non-zero but the average velocity is zero. The same test explains why uniform circular motion counts as accelerated motion: the speed never changes, but the velocity does, because its direction is changing continuously. Note also that both quantities carry the same SI unit, metres per second, so units alone will never separate them.

• A scalar has magnitude only; a vector has magnitude and direction and follows vector addition.
• Speed is distance divided by time and is a scalar; velocity is displacement divided by time and is a vector.
• Both speed and velocity are measured in metres per second in SI units.
• In uniform circular motion the speed is constant but the velocity is not, because the direction keeps changing.
• Over any closed path the average velocity is zero while the average speed is not.

• Treating speed and velocity as synonyms, as everyday speech does.
• Assuming that constant speed implies constant velocity — circular motion disproves it.
• Calling distance a vector because it shares its unit, the metre, with displacement.

As this direct classification, or applied — a round-trip or circular-track problem in which distance and displacement have to be separated.

• practice — not a real PYQ

  Which one of the following is a vector quantity?

  • (a)Distance
  • (b)Speed
  • (c)Displacement
  • (d)Time

  Answer(c) Displacement — it has both magnitude and direction; the other three have magnitude only.

• practice — not a real PYQ

  A body moves once around a circular track of radius r and returns to its starting point. Its displacement and the distance it has covered are respectively

  • (a)2πr and zero
  • (b)zero and 2πr
  • (c)2πr and 2πr
  • (d)zero and zero

  Answer(b) zero and 2πr — the start and finish coincide, so displacement is zero, while the path length is the full circumference.