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.