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A particle moving in a straight line is acted upon by a force which works at a constant rate and chages ist melocity from (u and v ) over a distance x. Prove that the taken in it is `3/2 (u+v)x/(u^(2)+v^(2)+uv)` . |
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Answer» Correct Answer - A From work-energy principle, `W=DeltaKE` `:. Pt=1/2m(v^(2)-u^(2)) (P="power")` or `t=m/(2P)(v^(2)-u^(2))` Further `F.v=P` `:. m.(dv)/(ds).v^(2)=P` or `int_(u)^(v)v^(2)dv =P/mint_(0)^(x)` `:. (v^(3)-u^(3) =(3P)/m.x` or `m/P =(3x)/(v^(3)-u^(3)))` Substituting in Eq. (i) `t=(3x(u+v))/(2(u^(2)+v^(2)+uv))` Hence proved. |
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