A particle is moving at t=0 from origin along the (+ve) direction of x axis.its speed depends on the distance travelled x as V=k√x.if v=dv/dx and a=dx/dt then find x,v and a in terms of time?
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Answer
v = b\sqrt{x}v=b
x
\dfrac{dv}{dt} = \dfrac{b}{2\sqrt{x}} \dfrac{dx}{dt}
dt
dv
=
2
x
b
dt
dx
a = \dfrac{bv}{2\sqrt{x}}a=
2
x
bv
a = \dfrac{dv}{dt} = a = \dfrac{b^2}{2}a=
dt
dv
=a=
2
b
2
v = \dfrac{b^2}{2}\tauv=
2
b
2
τ
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