How do you determine the direction of the acceleration?

Imagine watching a friend throw a ball to another friend as shown in the diagram below.� Because of gravity, the ball doesn�t follow a straight line.� In fact, if the drag from air can be ignored, then the ball follows a path that is shaped like a parabola.� This parabolic path is called the �trajectory� of the ball.�

Now compare the trajectory in the diagram above to the y vs x graph for the same ball that is shown below.�

They appear to be identical because they are.� Both represent a plot of the vertical coordinate y vs the horizontal coordinate x of the ball.� In short, a y vs x graph of a motion is identical to the trajectory in a photograph of that motion.�

The acceleration in the ball-throwing example above is constant and is the earth�s freefall acceleration.� Its direction is straight down.� All of the accelerations in this simulation are also constant so result in parabolically shaped trajectories.� The direction of such accelerations will always be in the direction that the parabola opens.�

One difficulty that you will likely encounter is that the y vs x graphs that you see may only show a portion of a parabola, not the entire parabola.� The portion that is displayed may not even include the vertex of the parabola.� In such cases, it is more difficult to determine the exact direction in which the parabola opens.� Keep in mind, however that the component of the velocity perpendicular to the acceleration will be constant.� For example, if the acceleration points vertically, then the horizontal spacing between the data points will be uniform.� If the acceleration points diagonally, then the data points will be spaced uniformly in the direction of the opposite diagonal.� Hence, if it is difficult to determine the direction in which the parabola opens, try to determine the direction in which the data points are uniformly spaced.�