How do you determine the direction of the acceleration from a v_y vs. v_x graph?

 

The definition of the x-component of the average acceleration is

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Since the acceleration in this simulation is constant, the acceleration (i.e., the instantaneous acceleration) is equal to the average acceleration.� Since time intervals (i.e., Dt) are always positive, the sign of a_{avg x} is always the same as the sign of Dv_x.� On a v_y vs. v_x graph, Dv_x �is positive when the final data point lies to the right of the initial data point since this means that the final v_x is larger than the initial v_x.� Hence:

�       a_x is positive when the line of data points stretches to the right of the initial data point.

�       a_x is negative when the line of data points stretches to the left of the initial data point.�

�       a_x is zero if the line of data points don�t stretch left or right of the initial data point.

 

Similarly:

�       a_y is positive when the line of data points stretches above the initial data point.

�       a_y is negative when the line of data points stretches below the initial data point.�

�       a_y is zero if the line of data points don�t stretch above or below the initial data point.

f

The acceleration selector is a graph of a_y vs. a_x.� The selector only has one choice for the magnitude of the acceleration in each direction.� Hence, knowing the signs of a_x and a_y is sufficient for selecting the correct acceleration.�