Integrating Acceleration to Find Velocity

[Anti-Meson]

Homework Statement

I intend to use the Runge-Kutta method but to do so I need to be able to find the velocity $$\frac{dx(t)}{dt}$$ from the acceleration and I need some pointers on how to get that from the equation below. In other words I am having difficulty integrating the equation wrt time.

Homework Equations

$$\frac{d^{2}x(t)}{dt^{2}} = \frac{k}{x(t)^{2}}$$

where k is a constant.


Any help would be appreciated. Thank-you.

 

[Dick]

I don't think you can express the velocity in any easy form. Isn't the usual trick to add dx(t)/dt=v(t) to your list of equations and make the first equation dv(t)/dt=k/x(t)^2 and solve that first order system of equations with Runge-Kutta?

 

[dacruick]

dont you need x(t)²??

 

[Anti-Meson]

I don't think you can express the velocity in any easy form. Isn't the usual trick to add dx(t)/dt=v(t) to your list of equations and make the first equation dv(t)/dt=k/x(t)^2 and solve that first order system of equations with Runge-Kutta?

The problem is Runge-Kutta method uses two variables, in my case x and t, though at the moment I only have 1 variable x as expressed in the equation of acceleration.