How do you determine the direction of the initial velocity from a y vs. x graph?

 

To state the obvious, horizontal position is plotted on the horizontal axis of a y vs x graph and vertical position is plotted on the vertical axis.� This is no different than what would be �plotted� if it were possible to take a photograph of a moving object�s path or trajectory.�

 

Notice that the first part of the y vs x graph for the current problem is a straight line.� There are four possible ways this can happen.� The diagrams below illustrate three of the four ways.� All three examples involve a ball�s motion near the earth, because the freefall acceleration from the earth is constant just as the acceleration is constant for the motions in this simulation.� Notice that in all three examples, the distance between the data points increases as the ball falls.� In each picture, the initial location of the ball is illustrated by the black data point.�

 

 

Straight line motion occurs when:

�       the initial velocity is zero and the acceleration is not zero as illustrated in the first picture.� Notice that the black initial dot and the next red dot are very close together.

�       the initial velocity and the acceleration have the same direction as illustrated in the second picture.� The biggest difference between the first and second picture is that the distance between the black and first red dots in the second picture is bigger than in the first picture.

�       the initial velocity and the acceleration have opposite directions as illustrated in the third picture.� This case is easy to identify because the black dot does not lie at one end of the string of dots.� The direction of the initial velocity is toward the location where the ball turns around.�

 

The fourth way that a y vs x graph can be straight is if the object has a non-zero initial velocity while the acceleration is zero.� The string of red data points in this case will be uniformly spaced.� The direction of the initial velocity will be the direction in which the red data points stretch.�

 

Be aware that in the rocket simulation, the string of data points in not likely to form a vertical straight line because the rocket is moving under the influence a thrust force which likely will not be directed downward as was the case with the examples above.�