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For a particle in rectilinear motion a=0.05V2m/s2,at  v=20m/s,x=0, Find x at v = 15 m/s and acceleration at x = 50m.
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Given that

a=0.05v2(i)

We know that,

v=dxdta=dvdtva=dxdvvdvdx=avdvdx=0.05v2dx=dv5=20dvv(ii)

At v=20m/s, x=0. Hence x at 15m/s is given by

x=1520dv0.05v=20ln(1520)x=5.754m   at   v=15m/sAns

Also from (ii):-

500dx=v2020dvv50=20ln(v20)v20=e5/2v=20e5/2(at  x=50m)a=0.05(v)2=0.05(20e5/2)2a=0.135m/s2(at  x=50m)Ans

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