# PLEASE PLEASE PLEASE Explain each part of the solution process. I'm trying to learn this and...

###### Question:

PLEASE PLEASE PLEASE Explain each part of the solution process. I'm trying to learn this and not just get an answer. I appreciate the help!!

A new speedboat with mass m is traveling at v0 at some zero time when its engine is shut off. The magnitude of the frictional force fk between the boat and water is proportional to the speed v of the boat. As an equation, the magnitude of fk is equal to v, where v is in meters per second, fk is in newtons, and is a constant with units of kilograms per second. Assume the boat is moving at speed v at some generic time t. These quantities are known as the base variables.

1. Draw a free-body diagram of the boat when it is slowing down in the water. In this drawing, show the mass, all the acting forces in the proper directions, the direction of motion, and the direction of the acceleration for the speedboat.

2. Find the acceleration a of the speedboat as a function of velocity v and other variables. Is the acceleration constant in time? Carefully explain your answer.

3. Find the velocity v of the speedboat as a function of the base variables, except the acceleration a.

4. Find the position x of the speedboat as a function of the base variables.

5. Find the effective coefficient of friction (k) for the speedboat in the water as a function of the base variables.

6. Sketch your derviced expressions for v and x as functions of time t. Indicate the values for each at t=0 and as t goes to infinity.

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