In summary: Sorry theIn summary, the conversation is about a physics problem involving a projectile fired into a viscous liquid. The retarding force is proportional to the square of the velocity, leading to a differential equation that needs to be solved in order to find the distance and time required for the projectile to reduce its velocity to half of its initial velocity. One person has found the expression for the distance and time, but is unable to solve for the first part of the problem. They have tried using the equation for constant acceleration but it does not apply in this case. The other person suggests using "separation of variables" to solve the differential equation, but the person struggling with the problem is not familiar with this technique. They continue to ask for guidance and
Supposedly you got the velocity, and then all you've written about getting the position is "failure failure failure."
Here's a hint: Try again.
The relationship between acceleration and velocity is analogous to that between velocity and position. If you understood how to get v from a, it's exactly the same mathematical process to get x from v.