CDS (II) 2021 General Knowledge · Question 6 of 120

Correct — D, 0 m, 100 m. Displacement is the shortest distance from the starting position to the finishing position, so the only thing that matters is where the athlete ends up, not how far they ran to get there. One lap takes 20 s. In 1 minute — 60 s — the athlete completes exactly three laps and is back at the start, so the finishing point coincides with the starting point and the displacement is zero, even though 300 m of track has been covered. In 10 s the athlete has run half a lap and is standing at the point diametrically opposite the start. The straight-line distance between those two points is the diameter of the circle, 100 m. Reading the two answers in the order the stem asks for them gives 0 m and then 100 m. Note that the number 100 turns up here as a diameter, not as a radius and not as an arc length: the half-lap path length is half the circumference, about 157 m, which is not among the options and is not what was asked.

• (a)0 m, 50 m — The first value is right and the second is the radius. After half a lap the athlete is a full diameter from the start, not a radius.
• (b)300 m, 100 m — 300 m is the distance covered in three laps, not the displacement. Ending where you started makes the displacement zero however far you have run.
• (c)300 m, 50 m — Wrong on both counts — it swaps displacement for distance in the first value and uses the radius instead of the diameter in the second.

Distance is the total path length covered and never decreases; displacement is the shortest distance measured from the initial to the final position, and it carries a direction. On any closed path the displacement over a whole number of laps is zero while the distance is not, and that gap is the whole point of keeping the two quantities separate. Speed is built on distance, velocity on displacement, which is why an athlete running laps has a positive average speed and zero average velocity.

The item pairs a whole number of laps with a half lap so that both traps can be laid at once. Sixty seconds divides exactly by twenty, which is the signal that the runner is back at the start; the moment the division comes out whole, the answer to that part is zero. Ten seconds is half of twenty, and the half-lap position is the one place on a circle where the straight-line separation is a maximum, equal to the diameter. Reaching for the radius here is the commonest slip, because the number 50 sits so naturally with a diameter of 100. Read the stem carefully on units too: the track is described by its diameter, not its radius, so no halving is needed at all.

• Displacement is the shortest distance from the initial to the final position; distance is the whole path length travelled.
• The magnitude of displacement can be zero while the distance covered is large — a closed loop is the standard example.
• For a circular track, the maximum possible displacement is the diameter, reached after an odd number of half laps.
• One lap of the given track takes 20 s, so 60 s is exactly three laps and 10 s is exactly half a lap.
• Half the circumference of a 100 m-diameter track is about 157 m, which is the distance covered in 10 s — not the displacement.

• Reporting the distance covered when the stem asks for displacement.
• Using the radius where the diameter is called for after half a lap.
• Reading '1 minute and 10 s' as a single interval of 70 s; the word 'respectively' shows they are two separate instants.

Almost always as a circular track with a lap time, asking for distance and displacement at a stated instant; sometimes as a walk in several compass directions with the net displacement to be found.

• practice — not a real PYQ

  A cyclist rides once around a circular park of radius 70 m and returns to the starting point. The distance covered and the magnitude of the displacement are respectively

  • (a)440 m and 140 m
  • (b)440 m and 0 m
  • (c)0 m and 440 m
  • (d)140 m and 440 m

  Answer(b) 440 m and 0 m — the circumference is about 440 m, but the finishing point is the starting point, so the displacement is zero.

• practice — not a real PYQ

  For an object moving along any path, which one of the following is always true?

  • (a)Displacement is greater than distance
  • (b)Distance is never less than the magnitude of displacement
  • (c)Distance and displacement are always equal
  • (d)Displacement can never be zero

  Answer(b) Distance is never less than the magnitude of displacement — the two are equal only for motion in a straight line without reversal.