How to tell which function has distance proportional to time?

[gurpalc]

Homework Statement

http://imgur.com/aYCc9

also in attachment

Homework Equations

n/a

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?

 

[CWatters]

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.

 

[CWatters]

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.

 

[CWatters]

The expression "proportional to time" is normally taken to mean "proportional to time¹ and excludes other powers such as timeⁿ, time^1/n etc

 

[gurpalc]

Thanks everyone for the replies. I got it now.