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For a particle in rectilinear motion a= -0.05V2 m/s2, at v=20 m/s, x=0. Find x at v=15 m/s and accn at x=50 m.
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a=0.05v2\[2ex]vdvdx=0.05v2dvv=0.05dx\[2ex]logv=0.05x+c.....(1)   at x=0;v=20.....put in (1) C=ln(20)=3   (i) x=?;v=15 logv=0.05×x+3\[2ex]log1530.05=xx=5.84m   (ii) a=?;x=50 logv=0.05×x+3\[2ex]v=e0.05×50+3=e0.5=1.65m/s\[2ex]a=0.05v2=0.05×1.652=0.14m/s2

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