NDA (I) 2018 General Ability Test · Question 53 of 150

Correct — B, Its speed changes with time. Velocity is a vector, so calling it constant fixes two things at once — its size and its direction. The size of the velocity is the speed. If the velocity is not changing, then neither is the speed, so a statement that the speed changes with time flatly contradicts the premise. Every other option follows from the premise instead of contradicting it, which is why (b) is the one that is not correct.

• (a)Its motion is along a straight line — Correct, and it follows from the direction half of the definition. A body turning a corner is changing the direction of its velocity even at unchanged speed, so constant velocity leaves it no option but a straight path.
• (c)Its acceleration is zero — Correct. Acceleration is the rate of change of velocity, and if the velocity is not changing that rate is zero. By Newton's first law the net force on such a body is zero too.
• (d)Its displacement increases linearly with time — Correct. With velocity fixed, displacement equals velocity multiplied by time, so a graph of displacement against time is a straight line whose slope is the velocity.

Speed is a scalar — it has size only. Velocity is a vector — it has size and direction, and the size of the velocity is the speed. A body has constant velocity when both parts stay fixed, which forces the path to be straight, the acceleration to be zero and the displacement to grow in direct proportion to time. Constant speed is a weaker condition, since a body can hold its speed while changing direction, as in uniform circular motion.

The item rewards a candidate who reads 'constant velocity' as the strong statement it is. A common way to go wrong is to think of a car on a highway holding a steady speedometer reading and then to accept that the speed 'changes' because the driver is going round a bend — but that scenario is constant speed, not constant velocity. Work the other way instead. Write down what constant velocity forbids: no change in size, no change in direction. Option (b) breaks the first, so it is the odd one out, while (a), (c) and (d) are three different consequences of the same premise. Uniform circular motion is the standard counter-example to keep in mind, because there the speed is constant, the velocity is not, and the acceleration is famously non-zero even though nothing speeds up.

• Speed is a scalar quantity; velocity is a vector with both magnitude and direction.
• Constant velocity implies zero acceleration and, by Newton's first law, zero net force.
• In uniform circular motion the speed is constant while the velocity changes continuously, because the direction changes.
• For constant velocity the displacement-time graph is a straight line and the velocity-time graph is a horizontal line.
• Average velocity over a round trip is zero because the displacement is zero, even though the average speed is not.

• Treating constant speed and constant velocity as the same condition.
• Assuming zero acceleration means the body is at rest rather than moving steadily.
• Forgetting that a change of direction alone counts as acceleration.

Set as a statement-screening item on the definition of velocity, or by giving a round trip and asking for the average velocity as against the average speed.

• practice — not a real PYQ

  A body moves round a circular track at a steady 10 m/s. Which statement is correct?

  • (a)Its velocity is constant
  • (b)Its acceleration is zero
  • (c)Its speed is constant but its velocity is not
  • (d)Both speed and velocity change

  Answer(c) Its speed is constant but its velocity is not — the direction of motion changes at every instant, so the velocity changes and there is a centripetal acceleration.

• practice — not a real PYQ

  For a body moving with constant velocity, the velocity-time graph is

  • (a)a straight line through the origin with positive slope
  • (b)a straight line parallel to the time axis
  • (c)a parabola
  • (d)a curve rising steeply

  Answer(b) a straight line parallel to the time axis — the velocity has the same value at every instant, so the graph has zero slope.