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The particle moves in a straight line so that it's distance s from a fixed point on itself at any instant is proportional to tn .If the velocity and acceleration are v and a respectively show that V2 =nav/n-1 |
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Answer» Given s∝tn ⇒ S = ktn Velocity v = \(\frac{ds}{dt}\) = \(\frac{d}{dt}\) (ktn) = kntn-1 a = \(\frac{dv}{dt}\) = \(\frac{d}{dt}\) (Kntn-1).Kn(n-1)tn-2 ⇒ \(\frac{a}{(n-1)}\) = kntn-2 ⇒\(\frac{a}{(n-1)}\)x ns = kntn-2n.s = kntn-2.nktn = k2n2t2n-2 = (Kntn-1)2 = v2 [∵ v = Kntn-1] ∴ \(\frac{nas}{(n-1)}\) = v2 |
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