What are the velocity & position of an object as function of time?

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Homework Help Overview

The problem involves a motorboat that experiences a sudden stop due to a frozen motor and subsequently slows down under a frictional force. The discussion focuses on determining the velocity and position of the boat as functions of time, as well as analyzing the boat's deceleration from a specific speed over a given time period.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of equations related to exponential decay to describe the boat's velocity and position. There are inquiries about how to derive the constant b/m from the provided information, and attempts to set up equations based on the initial and final velocities over time.

Discussion Status

Participants are actively engaging with the problem, exploring different equations and relationships. Some have provided equations based on the initial conditions, while others are questioning how to proceed with finding the necessary constants. There is no explicit consensus yet, but the discussion is progressing with various interpretations being explored.

Contextual Notes

Participants are working with specific values for initial and final velocities, as well as a time frame for deceleration. The need for additional information regarding the constant b/m is highlighted, indicating a potential gap in the problem setup.

DANIneplanets
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Homework Statement


A motorboat is moving across a lake at a speed vo when its moot suddenly freezes up and stops. The boat then slows down under the frictional force fR = -bv (a) What are the velocity and position of the boat as a function of time? (b) If the boat slows down from 4.0 to 1.0 m/s in 10s how far does it travel before stopping?

Homework Equations


fr=-bv

The Attempt at a Solution


v=v0 e-b/m *t
x=x0+ v0m/b (1-e -b/m *t)
 
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Now use the information from part (b) to find the constant b/m
 
how can i find b/m??
 
Put the given information into equations:
v0e(-b/m)T = 4 m/s
v0e(-b/m)(T+10) = 1 m/s
Then you can find how long it takes to stop (which will depend on v0)
 

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