A particle has initial speed u and its acceleration depends on speed according to a = k/v, where k>0. Its displacement in time T is:
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A particle has initial speed u and its acceleration depends on speed according to a = k/v, where k>0. Its displacement in time T is:

G1 Physics · Accepted Answer

From dv/dt = k/v, v dv = k dt. Integrating, v² = u² + 2kt. Hence x = ∫₀→T √(u²+2kt) dt. Let y=u²+2kt, so dy=2k dt. Then x = [1/(2k)]∫ y¹ᐟ² dy = [(u²+2kT)³ᐟ²−u³]/(3k).