Friction Force and Decelerating Boat

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Homework Help Overview

The discussion revolves around a physics problem involving a boat decelerating due to friction. The boat's mass is given, along with its initial and final speeds, and the frictional force is described as proportional to the boat's speed. Participants are tasked with determining the time required for the boat to slow down from 100 km/h to 45 km/h.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between acceleration and velocity, noting that the acceleration is not constant as it depends on the speed of the boat. There is mention of setting up a differential equation to describe the velocity change over time, but some express confusion about how to proceed without prior knowledge of differential equations.

Discussion Status

The discussion is ongoing, with participants exploring the implications of the non-constant deceleration and attempting to set up the necessary equations. Some guidance has been offered regarding the use of differential equations, but there is a lack of consensus on how to approach the problem given varying levels of familiarity with the concepts involved.

Contextual Notes

Some participants indicate that they have not yet learned differential equations, which may limit their ability to engage fully with the problem. There is an acknowledgment of the need to separate variables for integration, but uncertainty remains about how to correctly formulate the equations based on the problem's parameters.

Arman777
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Homework Statement


A 1000 kg boat is traveling at 100km/h when its engine is shut off.The magnitude of the frictional force ## \vec f_k## between boat and the water is proportional to the speed v of the boat:##f_k=70v##,where v is in meters per second and ##f_k## is in Newtons.Find the time required for the boat to slow to 45 km/h

Homework Equations


## \vec F=m \vec a##
##v-v_0=at##


The Attempt at a Solution


I turned km/h to m/s which its ##100km/h=27.7 m/s## and ##45km/h=12.5m/s##
then ;
##ma=-70v##
here the connfusing part is ##a## decreases when v decreases.there's no constant decelaration.I thought integral but without distance I stucked.
##∫mdv=∫-70vdt##

I don't know what to do.

Thank you
 
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Arman777 said:
##ma=-70v##
here the connfusing part is ##a## decreases when v decreases.there's no constant decelaration.I thought integral but without distance I stucked.

Indeed the deceleration is not constant. Note that ##a = dv/dt## and so what you have is a differential equation describing how velocity changes with time. You will need to solve this differential equation.
 
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Orodruin said:
Indeed the deceleration is not constant. Note that ##a = dv/dt## and so what you have is a differential equation describing how velocity changes with time. You will need to solve this differential equation.

I didnt learn diff equation.I am fresman student and uni teaches us second year.Like I have no clue
 
Arman777 said:
.I thought integral but without distance I stucked.
∫mdv=∫−70vdt
That's not the correct equation. You need to separate the variables.
So you can do integrals and differentials separately, right? I guess your only problem is to set up differential equations using the given data?
Arman777 said:
I didnt learn diff equation.I am fresman student and uni teaches us second year.Like I have no clue
As orodruin pointed out, use a=dv/dt.
What will be the equation of the force on the boat? Which force is acting on it?
 

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