How do I sketch a direction field for Newton's 2nd law with a constant added?

[XSK]

Homework Statement

(i'm not sure if this is the correct forum please move it if incorrect)
my problem is with generally drawing direction fields - i don't really know what to do. i have notes but i can't make head nor tail of them. this is an example of a question concerning them:

Homework Equations

i know that if you stick the requirments into Newton's 2nd law adding constant k you get that equation, and i know to find the terminal velocity you integrate and find v, but i don't know how to sketch the direction field.

The Attempt at a Solution

i see that

dv/dt = -g + k/m

but this seems to be independent of both v and t so how do i plot it as a graph?

even if there were a v or t in that equation i still wouldn't be comfortable to draw the direction field because i don't know what to do >_>;

thanks

 

[foxjwill]

Think of direction fields as a $${dy \over dx} = f(x,y)$$. At each point $$(x,y)$$ on the graph, you draw a tic-mark with slope equal to f(x,y). So here, instead of x and y, we have v and t, and f(v,t)=-g+k/m. What's the slope of each tick mark going to be?

 

[XSK]

uhh
i'm not sure...some kind of straight line?

 

[HallsofIvy]

Check the meaning of the word "slope". It is a number not "some kind of line". What does the slope of a line mean?

 

[XSK]

ok i looked up slope and now know it is a number but the answer to this question still eludes me!

i don't know how you'd put the equation on a graph

the notes i have for this involve looking at the independence of say, x of the equation so I am rather stumped. also i just suck at graphs...