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:

given:
radius of circle = 2 km
start point = P (top of circle)
end point = S (left side of circle)

step 1: what is displacement?

displacement = shortest straight-line distance between start and end
NOT the curved path along the circle

so we just need straight line PS

step 2: visualize positions

center = O

P is directly above O → distance 2
S is directly left of O → distance 2

so OP = 2 km (vertical)
OS = 2 km (horizontal)

and OP ⟂ OS (90° angle)

step 3: triangle OPS

you now have a right triangle:

OP = 2
OS = 2
PS = hypotenuse

apply Pythagoras:

PS² = OP² + OS²
PS² = 2² + 2²
PS² = 4 + 4 = 8

PS = √8 km

step 4: final understanding

even though cyclist moved along a curved path, displacement ignores path
it only depends on start and end points

so straight-line distance = √8 km