How to tell which function has distance proportional to time?

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Homework Help Overview

The discussion revolves around identifying which functions represent distance as proportional to time, based on graphical representations. Participants are analyzing different curves and their characteristics in relation to time and distance.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the characteristics of linear versus non-linear functions in relation to proportionality. Questions arise about the implications of curves not passing through the origin and the meaning of proportionality in mathematical terms.

Discussion Status

There is an active exploration of the definitions and characteristics of proportional relationships. Some participants provide insights into the mathematical form required for proportionality, while others question the implications of specific curves on the relationship between distance and time.

Contextual Notes

Participants note that the expression "proportional to time" typically refers to a linear relationship, excluding other powers of time. There is also mention of a specific example where distance appears to increase while time remains constant, raising questions about the interpretation of the curve.

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Homework Statement



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Homework Equations



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The Attempt at a Solution



I'm not sure how to tell when distance is proportional to time. My guess is it would be graphs a and b because they're both straight lines and when time increases, distance increases a set amount as well.

Also can you explain why the curve function does not have distance proportionate to time?
 

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a) Curve A and B show distance as a linear function of time.

b) I believe only curve A shows distance proportional to time. Curve B does not pass through the origin. Curve C isn't straight.

Regarding Curve C. The expression "in proportion" hints at constant ratio. So for it to be directly proportional the equation must be of the form

y/x = k
or
y = kx

where k is a constant called the constant of proportionality. K can be -ve or +ve.
 
Last edited:
Also can you explain why the curve function does not have distance proportionate to time?

See above. In addition, for this particular example only, on the right hand side the distance appears to be increasing while time remains constant. Putting aside the practicalities of achieving infinite velocity it shows that in this region of the curve distance appears to be independent of time.
 
The expression "proportional to time" is normally taken to mean "proportional to time1 and excludes other powers such as timen, time1/n etc
 
Thanks everyone for the replies. I got it now.
 

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