How Can I Calculate Position z(t) from Velocity as a Function of Position?

[henryc09]

Homework Statement

I have a problem where I have a force and therefore acceleration which depends on position, z. Using z'' = dv/dt = dv/dy * dy/dt = v*dv/dy I was able to find velocity as a function of position.

It nows asks for z(t). I'm having a bit of a mental block here and don't know how to go about finding this. Any help would be appreciated!

Homework Equations

The Attempt at a Solution

 

[Mark44]

Homework Statement

I have a problem where I have a force and therefore acceleration which depends on position, z. Using z'' = dv/dt = dv/dy * dy/dt = v*dv/dy I was able to find velocity as a function of position.

I'm confused by your choice of variables in this problem. The usual variables that are used in problems of this type are s for position, v for velocity, and a for acceleration, where v = ds/dt, and a = dv/dt = d²s/dt².

What does y represent in your problem?

It nows asks for z(t). I'm having a bit of a mental block here and don't know how to go about finding this. Any help would be appreciated!

 

[henryc09]

sorry I messed that up, wherever I put y I meant z.

so i found v(z)

 

[Mark44]

What do you have for v(z)? The usual thing to do with velocity to find position is to integrate, but for that you would need to integrate with respect to time, and v would have to be a function of t.