A cyclist starts from the point P of a circular ground of radius 2 km and travels along its circumference to the point S. The displacement of a cyclist is:

Solution

Physics sir · 3 steps

Forget the long arc. Displacement only cares where you start and where you stop: P and S.

1. Path versus displacement. The cyclist rides P → Q → R → S, three quarters of the circle. That arc is the distance travelled. Displacement is the straight line from the start P to the end S.
2. Spot the right angle. OP points up and OS points left, so they are perpendicular at the centre O. Each is a radius of 2 km, and PS is the hypotenuse of right triangle POS.

   PS = √(OP² + OS²) = √(2² + 2²) = √8 km

3. So. The displacement is √8 = 2√2 ≈ 2.83 km, option (a).

The idea to keep. Displacement is the straight line from the first point to the last. On a circle, two points a quarter-turn apart are r√2 apart, whichever way round you went.

Answer from the NTA final answer key. Solution by PrepWiser.