What is the velocity of a decelerating boat after 4.9 seconds?

[Lenart Kovac]

Homework Statement

A boat, moving at the velocity of 9,9m/s turns off its engine and starts decelerating at the rate of a=-kv^2. What is the velocity of the boat after 4,9 seconds if the constant k is k=5,5m

Homework Equations

The Attempt at a Solution

I tried to integrate deceleration to get velocity, which got me the equation v= -k * t * v0^2, but that got me a really weird number and I'm sure I'm not doing something right, so I'm asking you for help

 

[scottdave]

This is a separable differential equation. The way you need to integrate is like this: First, note that a = dv/dt, so we have dv/dt = -k*v².
Rearrange so that you have this
$$dt = \frac {dv} {-k v^2},$$
Now you can integrate both sides. If you don't want to fool with integration constant, then you can integrate the right side (with velocity) from 9.9 m/s to v_f and integrate the left side (time) from 0 seconds to 4.9 seconds. Then you can rearrange to solve for v_f

 

[scottdave]

I made a revision, it seems I had my left side and right side switched around Also I used some LateX so it would look a little nicer.

 

[Lenart Kovac]

It worked! Thanks for the help :)