# Solving Boat Motor Engine Equations w/ Integration

• betty0202
In summary, the problem involves finding the velocity of a motorboat with a constant engine force and drag force due to the water. Using the equations of motion and integration, the final solution is v = (e^(-t/m) + k)/c.
betty0202

## Homework Statement

turning on the engine of a motorboat (v0=0),
K = constant force due to the engine
drag force of the water D = -cv
find v(t)=?

integration
f=ma, a=dv/dt

## The Attempt at a Solution

[/B]
D+K = MA
K-cv = MA
(A=dv/dt)
K-cv=Mdv/dt
Mdv=dt(K-cv)
?
i want to do integration on both side of the
equation but I can't isolate V

thanks

betty0202 said:
Mdv=dt(K-cv)
You need only gather the v and t terms on opposite sides of the equation. Constants can be on either side. Divide both sides by (K - cv).

betty0202
gneill said:
You need only gather the v and t terms on opposite sides of the equation. Constants can be on either side. Divide both sides by (K - cv).

I hope I did the math right ## \int_{}^{} (\frac{m}{k-cv})dv=\int_{}^{}dt ##
## -m\ln(cv-k)=t ##
## \ln(cv-k)=-\frac{t}{m} ##
## v=\frac{e^{-\frac{t}{m}}+k}{c} ##
??

You'll want to write the integrals as definite integrals (with specified limits of integration), otherwise you need to introduce and deal with the constants of integration. The starting limits for each integral are simple: they're both zero.

betty0202
gneill said:
You'll want to write the integrals as definite integrals (with specified limits of integration), otherwise you need to introduce and deal with the constants of integration. The starting limits for each integral are simple: they're both zero.
thank you

## 1. How do you solve boat motor engine equations using integration?

To solve boat motor engine equations using integration, you will need to first determine the initial conditions of the boat and the motor, such as the initial velocity and acceleration. Then, you can use the laws of motion, such as Newton's Second Law, to set up the equations. After that, you can use integration techniques, such as separation of variables or substitution, to solve for the unknown variables.

## 2. What is the purpose of using integration in boat motor engine equations?

The purpose of using integration in boat motor engine equations is to determine the motion of the boat and the forces acting on it. Integration allows us to find the exact values of important variables, such as position, velocity, and acceleration, which are crucial in understanding the behavior of a boat.

## 3. Are there any specific techniques for solving boat motor engine equations using integration?

Yes, there are specific techniques for solving boat motor engine equations using integration. Some common techniques include separation of variables, substitution, and integration by parts. It is important to choose the appropriate technique depending on the form of the equation and the variables involved.

## 4. Can boat motor engine equations be solved without using integration?

In some cases, boat motor engine equations can be solved without using integration. However, integration allows for a more accurate and precise solution, especially for complex equations. It also allows us to take into account factors such as air resistance and water currents, which can significantly affect the motion of a boat.

## 5. How can boat motor engine equations using integration be applied in real-world situations?

Boat motor engine equations using integration can be applied in real-world situations, such as designing and optimizing boat engines, predicting the performance of a boat in different conditions, and understanding the forces acting on a boat during navigation. This can also be useful in marine engineering and naval architecture to improve the design and efficiency of boats.

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