CDS (II) 2023 General Knowledge · Question 2 of 120

Correct — B, vb > va > vc. The journey is drawn as a graph in three straight-line parts, and the whole question is about slope. On a distance–time graph the speed of the car is the gradient of the line — how much distance it gains for each second that passes — so comparing va, vb and vc means comparing how steeply the three parts rise, and nothing else. Length of a part tells you only how long that stage lasted or how far it went, not how fast it was. Ranked by steepness the printed journey runs B first, then A, then C: the middle stage is the steepest climb, the opening stage rises more gently, and the closing stage is the flattest of the three. That gives vb greater than va, and va greater than vc, which is option (b).

• (a)va < vb < vc — Puts the fastest stage last. It would need the graph to get steeper and steeper from left to right, so that the closing stage outran the middle one — the reverse of what is drawn.
• (c)va = vb = vc — Equal speeds would mean one single straight line of unchanging gradient from start to finish. The paper would then have had no reason to split the journey into three named parts at all.
• (d)va > vb ; va > vc — Claims the opening stage is the fastest. Half of it is true — A does beat C — but A does not beat B, and this option is built for a candidate who spots only that the last stage is slow.

Motion graphs carry their information in their gradient and their area. On a distance–time graph the gradient is speed, a horizontal line means the body is at rest, and a curve means the speed is changing. On a velocity–time graph the gradient is acceleration instead, and it is the area under the line that gives displacement. Confusing the two families of graph is the single most common error in this part of mechanics.

This is a read-the-graph item, so the graph is doing the work and no amount of algebra will replace it — the bank that holds this paper stores the printed text, and the picture itself sits only in the booklet, which is worth knowing if you are drilling from a text file rather than the original. The method, though, is fixed and can be practised without it. Identify which quantity is on which axis, remember that distance against time gives speed as the gradient, then rank the segments by steepness and match that ranking to the options. Steeper always means faster; a flat stretch means a halt. Candidates lose this mark by ranking the segments by how long they look on the page rather than by how sharply they rise.

• On a distance–time graph the speed is the gradient, that is the distance gained divided by the time taken.
• A horizontal stretch on a distance–time graph means the object is stationary, not that it is moving slowly.
• A straight line on a distance–time graph means uniform speed; a curve means the speed is changing.
• On a velocity–time graph it is the gradient that gives acceleration and the area beneath the line that gives displacement.
• Speed is a scalar and uses total path length; velocity is a vector and uses displacement, which is why the two can differ over the same journey.

• Reading a distance–time graph as though it were a velocity–time graph, so that a rising line is mistaken for acceleration.
• Judging speed by how long a segment looks on the page instead of by how steeply it rises.
• Treating a flat portion of a distance–time graph as slow, uniform motion when it actually means a halt.

Nearly always as a graph to be read — rank the speeds, name the stage of rest, or pick the graph that matches a described journey.

• practice — not a real PYQ

  A distance–time graph for a moving body is a straight line parallel to the time axis. What does this indicate?

  • (a)The body is moving with uniform speed
  • (b)The body is at rest
  • (c)The body is uniformly accelerated
  • (d)The body is moving with increasing speed

  Answer(b) The body is at rest — time passes but the distance from the starting point does not change, so the gradient, and hence the speed, is zero.

• practice — not a real PYQ

  For a body in motion, the slope of a distance–time graph gives which one of the following quantities?

  • (a)Acceleration
  • (b)Displacement
  • (c)Speed
  • (d)Momentum

  Answer(c) Speed — the slope is distance gained per unit time, which is the definition of speed. Acceleration is the slope of a velocity–time graph instead.