Graphical analysis of data is an important part of science.  When motion is analyzed using data from an experiment, a relationship is sought.  The relationship is evident when observing the data points (click here to see an example of data manipulation). 

When a hypothesis is made by an assumption of the nature of a relationship, an equation can be extracted from the resulting graph.

For an object moving with constant acceleration, a displacement vs. time graph will produce a parabola with the equation:

d = v_it + ½ at²

For an object moving with constant acceleration, a velocity vs. time graph will produce a straight line with the equation:  

v_f = v_i + at

For an object moving with constant acceleration, the acceleration vs. time graph will produce a horizontal line.

The instantaneous velocity (at a specified time value) of the object can be found by reading the value off of the velocity vs. time graph, or by finding the slope of the displacement vs. time graph at the desired time value.

The acceleration (at a specified time value) of the object can be found by reading the value off of the acceleration vs. time graph, or by finding the slope of the velocity vs. time graph at the desired time value.

Kinematics 11 Links