A meteorite travelling through space enters a cloud of gas. The initial speed is #u# , and after penetrating the cloud by a distance of #x# the deceleration is #kx^2# . Find the distance the meteorite penetrates?

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Answer 1 · 2018-06-17T10:18:54

#a = v (dv)/(dx) = - k x^2 #

Separating and integrating:

#int_u^(v(x)) v \ d v = - k int_0^x \ x^2 \ dx#

#v^2/2 - u^2/2= - k/3 x^3 #

Upon meteorite coming to rest:

#implies bb( x = root3((3 u^2)/(2k)) )#