A particle moves unidirectionally on a horizontal plane under a constant-power energy source. Which displacement-time graph describes the motion? Image
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Question

A particle moves unidirectionally on a horizontal plane under a constant-power energy source. Which displacement-time graph describes the motion? Image

G1 Physics · Accepted Answer

Constant power P gives dK/dt=P, so (1/2)mv²∝t and v∝√t. Therefore x=∫vdt∝t³ᐟ²: an increasing curve with increasing slope and zero initial slope. This corresponds to Image 3. Hence option C.