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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.
1 Answer
written 8.7 years ago by |
Given that
a=−0.05v2−−−−−−−−−(i)
We know that,
v=dxdta=dvdt∴va=dxdv∴vdvdx=a∴vdvdx=−0.05v2∴dx=−dv5=−20dvv−−−−−−−−−−−−(ii)
At v=20m/s, x=0. Hence x at 15m/s is given by
x=−15∫20dv0.05v=−20ln(1520)∴x=5.754m at v=15m/s⇒Ans
Also from (ii):-
50∫0dx=v∫20−20dvv∴50=−20ln(v20)∴v20=e−5/2∴v=20e−5/2(at x=50m)∴a=−0.05(v)2=−0.05(20e−5/2)2∴a=−0.135m/s2(at x=50m)−−Ans