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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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written 3.9 years ago by |
a=−0.05v2\[2ex]∴vdvdx=−0.05v2⟹dvv=−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]∴log15−3−0.05=x⟹x=5.84m (ii) a=?;x=50 logv=−0.05×x+3\[2ex]∴v=e−0.05×50+3=e0.5=1.65m/s\[2ex]a=−0.05v2=−0.05×1.652=−0.14m/s2