An object is in uniform circular motion on a plane. Suppose that you measure its displacement from the centre along one direction, say, along the x- axis. Which one among the following graphs could represent this displacement (x)?

An object in uniform circular motion has a projection on any diameter that follows simple harmonic motion (SHM). When measuring the displacement (x) from the center along the x-axis, the position is given by the sinusoidal function x(t) = R cos(ωt + φ). This relationship demonstrates that while the particle moves in a circle, its shadow or projection on a linear axis oscillates back and forth between +A and -A. The resulting graph of displacement versus time is a pure harmonic wave, typically a sine or cosine curve. Among the standard representations of such motion, Graph I (implied as the sinusoidal wave) correctly depicts this periodic, wavelike character. Other non-sinusoidal graphs, such as linear zig-zags or pulses, do not accurately represent the smooth acceleration and velocity changes inherent in the projection of circular motion.