How do you determine the direction of the initial velocity from v_x vs. t and v_y vs. t graphs?

 

A v_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 a v_x vs. t graph.� The opposite is true for a v_y vs. t graph.� No information about the horizontal component of a motion can be gleaned from a v_y vs. t graph.�

 

Both v_x vs. t and v_y vs. t graphs are velocity 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 a v_x vs. t graph but could just as easily refer to a v_y vs. t graph.

 

On a v_x vs. t graph, the vertical coordinate of a data point is equal to the x-component of the velocity of the object.� The x-component of the initial velocity, v_ox, is determined by the vertical coordinate at t=0s.� In the simulation, the t=0s data point is marked by a thick black border.�

 

Hence, to determine the sign of v_ox, determine the vertical coordinate of the initial point of the v_x vs. t graph.� Similarly, to determine the sign of v_oy, determine the vertical coordinate of the initial point of the v_y vs. t graph.�

 

The initial velocity selector is a plot of v_oy vs. v_ox.� Hence, knowing the signs of both v_ox and v_oy is sufficient to select the direction of the initial velocity with the selector.�