The trajectory of a particle is something we did not discuss for one-dimensional motion. The trajectory is the line in space along which the particle moves. You can imagine measuring this using a camera with very long exposure time. The picture taken shows the positions in space visited by the particle as it moved. What does the trajectory look like for motion in one dimensions? Just a line segment, and that is why we did not cover it for one dimensional motion.
In two dimensions the trajectory can be more interesting than that. For example if I throw this ball It follows a curved trajectory that looks something like this. (draw parabola on board). The trajectory is a diagnostic of motion which can be very important and useful but nonetheless does not contain the full information about the motion. This is because I have lost the information about when the particle was where along the trajectory.
Knowing mathematical expressions for x(t) and y(t) we can derive the trajectory. I will illustrate that with an example.
Problem 3
The position versus time for a tennis ball is given by
where
Will the ball get over the net which stands 1.1 m tall at 
m?
One way to go about this problem is graphically. I simply
put in a range of values for t and calculate the corresponding values for
x(t) and y(t). I get the following table
Now I can proceed to plot the data to the trajectory followed by the ball
to ascertain that the ball does clear the net. Note that information about
when the ball passes the net is not available in the trajectory.
A more elegant way to proceed is to derive a mathematical expression for the trajectory by eliminating t from the expressions and deriving how y depends on x.
For our example we get from the x-component of Eq. 13
We insert this expression for t in the y-component of Eq. 13
to get
This is the expression for the trajectory followed by the particle.
Inserting the position of the net 
m I can calculate
the height of the ball above ground to be
The conclusion again is that the ball does clear the net.