Understanding Trajectory Graphs

[mymabelline]

Trajectory Graphs??

Homework Statement

The trouble I'm having is with determining what information I can get from a trajectory graph and how that information differs from what I can find on a position vs. time graph. Is the acceleration I find just the rate of change in the direction of velocity? and is the tangental velocity equal to speed or do we just we use it to represent the direction of velocity?

The Attempt at a Solution

The only thing that I think I know for sure is that the slope of the trajectory graph gives the direction of velocity, but not the actual velocity. But I don't know why that is true, my book does a horrible job of explaining that.

 

[rock.freak667]

You trajectory graph will be of the form y=bx-ax².

So if you differentiate w.r.t t. you will get dy/dt = (b-2ax)dx/dt

dy/dt and dx/dt are both velocities, so you will get a velocity for the gradient.