A boat with initial speed vo is launched on a lake. The Boat is slowed by the water by a force F=-αeβv. Find an expression for the speed v(t), and find the time and distance for the boat to stop.
Drag force F=-αeβv
alpha and beta are not specified as to what they represent.
The Attempt at a Solution
I have an attached attempted solution, I'm just kind of confused on my results, I feel like it makes sense but at the same time it doesn't. My confusion lies in that I try to imagine using my derived v(t) equation but the drag force is constantly changed based on the instantaneous velocity at any moment, the v in the force equation is what throws me off, and makes me think I need to use a different approach.
Once I found my v(t) I found time when v(t)=0, then I found velocity as a function of position to find distance when v=0.
But again, now that I look at it, the v that is apart of e should probably be 0 as well, then the positions and times won't be affected by the drag force...