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Q3.9: NCERT Physics - Part 1 MOTION IN A PLANE 3.9 Solution: A cyclist starts from the centre O of a circular park of radius …
⚠️ Common Exam Traps & Conceptual Pitfalls
Students frequently read the diagram as a half‑circle and use the arc length $\pi r$ instead of the correct $\frac{\pi}{2}r$, inflating the total distance and average speed. Always identify the central angle shown (here $90^{\circ}=\pi/2$ rad) before converting it to arc length.
A cyclist starts from the centre O of a circular park of radius 1 km, reaches the edge P of the park, then cycles along the circumference, and returns to the centre along QO as shown in Fig. 3.20. If the round trip takes 10 min, what is the (a) net displacement, (b) average velocity, and (c) average speed of the cyclist?
Step-by-Step Verified Solution
**Answer:** (a) Net displacement = 0. (b) Average velocity = 0. (c) Average speed = 21.4 km/h.
**Step-by-Step Explanation:**
(a) The cyclist returns to the starting point O, so net displacement = 0.
(b) Average velocity = displacement/time = 0.
(c) Total path length = OP + arc PQ + QO = 1 + (�/2)(1) + 1 = 2 + �/2 = 3.57 km.
Average speed = 3.57/(10/60) = 21.4 km/h.
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