Hi, This is a Chegg problem/solution - I\'m confused how the lnC comes out of th

Question

Hi,

This is a Chegg problem/solution - I'm confused how the lnC comes out of the integral dv/v=-k dx why wouldn't it

be ln(v)=-kx + C ? Did he just shortcut the solution? Thanks

the acceleration of a particle is defined by the relation a =-kv2, where a is expressed in m/s2 and v inm/s. the particle starts at x = 0 with a velocity of 9m/s and whenx = 13m the velocity is found to be 7m/s. determine the distancethe particle will travel (a) before its velocity drops to 3m/s, (b)before it comes to rest

a = dv/dt = dv/dx dx/dt = v dv/dx = -kv2

dv/dx = -kv

dv/v = -k dx

ln(v) = -kx + lnC

x = 0, v = 9 m/s, ln9 = lnC

so

ln(v) - ln9 = -kx

x = k ln(9/v) (1)

x = 13 m, v = 7 m/s

13 = k ln(9/7) (2)

(1)/(2):

x/13 = ln(9/v)/ln(9/7)

x = 13 ln(9/v)/ln(9/7)

a) v = 3 m/s, x = 13 ln(9/3)/ln(9/7) = 57 m

b) v = 0, x -> %u221E

Explanation / Answer

after the integration there must be a constant, so that constant is c, however that can be represented as lnC. so for sake of simplicity he has taken lnC instead of c.

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