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## Homework Statement

The force acting on a particle of mass m is given by

F=kvx

in which k is a positive constant. The particle passes through the origin with the speed v naught at time t=0. Find x as a function of (t)

## Homework Equations

F=ma

a=(dx/dt)(dv/dx)

## The Attempt at a Solution

F=kvx

ma=kvx

a=kvx/m

(dx/dt)(dv/dx)=kvx/m

v(dv/dx)=kvx/m

dv/dx=kx/m

dv=(kx/m)dx

integral of both sides left in terms of dv and right in terms of dx

V-Vnaught=kx^2/2m

I'm not sure where to go from here. Help would be very much appreciated!