How do you determine the direction of
the initial velocity from x vs. t and y vs. t graphs?
An x vs t graph describes
the horizontal component of a motion only.�
No information about the vertical component of a motion can be gleaned
from an x vs. t graph.� The opposite is
true for a y vs. t graph.� No information
about the horizontal component of a motion can be gleaned from a y vs. t
graph.�
Both x vs. t and y vs. t
graphs are position vs. time graphs.� The
same rules that describe how to read information from one type of graph apply
to the other type of graph as well.� The
paragraph below refers to an x vs. t graph but could just as easily refer to a
y vs. t graph.
On an x vs. t graph, the
slope of the curve at a given instant is equal to the x-component of the
velocity of the object at that instant (i.e., vx).� Positive slopes correspond to positive values
of the x component of the velocity (i.e., vx
> 0).� Negative slopes correspond to vx < 0.�
A zero slope corresponds to vx =
0.� The x-component of the initial
velocity, vox, is determined by the slope
of the curve at t=0s.� In the simulation,
the t=0s data point is marked by a thick black border.�
Hence, to determine the
sign of vox, determine the slope of the x
vs. t graph at t=0s.� Similarly, to
determine the sign of voy, determine the
slope of the y vs. t graph at t=0s.�
The initial velocity
selector is a plot of voy vs. vox.�
Hence, knowing the signs of both vox
and voy is sufficient to correctly
select the direction of the initial velocity with the selector.�