Find velocity as a function of position x

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I am trying to find the velocity as a function of position for a particle of mass m that starts from rest and has a force acting on it equal to
F(x)= Fo+cx

My lecturer said that this would be an easy problem to solve but for whatever reason I am having trouble!

I have got as far as to say that

F(x)=m a(x)

So surely a(x)=F(x)/m

Then do I possibly integrate with respect to dx?
 

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Dick
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I am trying to find the velocity as a function of position for a particle of mass m that starts from rest and has a force acting on it equal to
F(x)= Fo+cx

My lecturer said that this would be an easy problem to solve but for whatever reason I am having trouble!

I have got as far as to say that

F(x)=m a(x)

So surely a(x)=F(x)/m

Then do I possibly integrate with respect to dx?

Integrating adx will not give you a velocity. Integrating adt would but that's not going to lead anywhere. You start by realizing a=dv/dt=(dv/dx)(dx/dt)=(dv/dx)v. If you use that then you get a separable differential equation in the variables v and x. Solve it.
 

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