Kinematic Equations: Relationships & Slopes

[bugsy25]

I'm a little confuse about these.
velocity as a function of time, displacement as a function of time
and velocity as a function of displacement. I know how to use this formulas, but in my lab there is a question that I am stuck on. How are this kinematic equations related to each other? and can you talk about each of their slopes?

 

[vaishakh]

You take an example in which you once draw graph for velocity constant then the acceleration constant. Looking at the graphs you will understand the things. In fact you can do even dimensional analysis.

 

[physlaw]

In the equation v = at, which is just from the definition of acceleration, if you assume that you know what the acceleration is, then you can get the final velocity at any time 't.' So we say that we know what v is as a function of time. Likewise, for the equation
v^2= 2 a (x-xo), (assuming here it starts from rest) you can find what an object's velocity is when it is at any position along the x axis. So we say we know velocity as a function of position. If you look up the derivation of this equation, you'll see it comes from basic principles beginning with the first equation and from the definition of average velocity.