Why Is Speed Proportional to the Square Root of Time in This Physics Problem?

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Homework Help Overview

The discussion revolves around a physics problem involving a particle starting from rest, acted upon by a net force that does work at a rate proportional to time. Participants are exploring the relationship between speed and time, particularly questioning why speed is proportional to the square root of time.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants attempt to relate power, work, and kinetic energy to derive the relationship between speed and time. Some express confusion over the proportionality of speed to time, while others question the interpretation of the problem statement regarding the force and work rate.

Discussion Status

The discussion is ongoing, with participants providing insights and corrections to their initial interpretations. There is a recognition of the importance of distinguishing between the force being constant and the work rate being proportional to time, which may lead to a clearer understanding of the relationship in question.

Contextual Notes

Some participants note a potential misunderstanding of the problem statement, specifically regarding the nature of the force and its relationship to time. This highlights the need for careful consideration of the definitions and assumptions involved in the problem.

NewtonGalileo
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Homework Statement



A particle starts from rest and is acted on by a net force that does work at a rate that is proportional to the time t. The speed of the particle is proportional to:

sq root of (t)

t

t^2

1/sq root(t)

1/t


Homework Equations



power = work / time
work = change in kinetic energy

The Attempt at a Solution


So,
(1/2 mv^2 / t) proportional to (t)
So,
v proportioanl to t

But, the answer key says v proportional to sq root of t. How is that?
 
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NewtonGalileo said:
power = work / time
work = change in kinetic energy

The Attempt at a Solution


So,
(1/2 mv^2 / t) proportional to (t)
Be careful here. Power is also equal to force times velocity.

In this particular problem, the force is proportional to t, as you know.

But the power is also proportional to velocity. But what is velocity?

Make the substitutions into force and velocity, and the answer should become more clear.
 
But,

net force is a constant. It is not proportional to time t.
I also looked at:
power = work/time = force x velocity
power ~ t
force x velocity ~ t
since force is a constant,
velocity ~ t

wouldn't this be right? why sq.root of t?
 
Perhaps you're right. I think I originally misinterpreted the problem statement as saying the force was proportional to t. But now I see it says that the rate of work is proportional to t. So yeah, that makes a difference.
 

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