This video adapted from the Encyclopedia of Physics Demonstrations explores how constant acceleration affects an object's motion. As a ball rolls down an incline, lights flash at one-second intervals, marking the position of the ball. Observe how the ball's position, velocity, and acceleration change as it rolls down the incline. Investigate its motion by plotting graphs of position versus time, average velocity versus time, and acceleration versus time.
For any moving object, there are clear relationships between its position, velocity (speed in a given direction), and acceleration (rate of change of velocity). By measuring an object's position over time, not only can you see how its location changes, you can also analyze its velocity and acceleration. A plot of measurements from a moving object gives a graphical representation of its motion in which the shape and slope of the line can reveal information.
For example, the shape and slope of the line on a position-versus-time graph reveals information about the object's velocity. Imagine a person walking at a constant pace in a straight line. After one second of walking, he is one meter from his starting point; after two seconds, he is two meters from his starting point; and after three seconds, he is three meters from his starting point. If the measurements of his position were plotted on a graph of position-versus-time, it would create a straight line. The slope of the line shows the difference in position over each time interval—the average velocity. In this case, there is a constant change in position over time and the line has a constant slope. In other words, the person is moving at a constant velocity.
The slope and shape of the line on a position-versus-time plot can therefore provide information about the object's velocity: a straight line (constant slope) means a constant velocity, a steep slope means a higher velocity, a slight slope shows a lower velocity, and a changing slope means a changing velocity.
Similarly, on a graph of velocity-versus-time, the slope of the line shows the change in velocity over each time interval—the acceleration. For example, the plot of the velocity of an object moving at a constant rate would form a horizontal line with zero slope, which represents zero acceleration. So the slope of the line on a velocity-versus-time graph can provide information about the object's acceleration: a constant slope means constant acceleration, a steep slope means a larger acceleration, a slight slope means a smaller acceleration, and a changing slope means a changing acceleration.
The slope of the graph of position-versus-time can be positive or negative, depending on the direction of the change. Similarly, the slope of velocity-versus-time can be either positive or negative. Negative velocities and accelerations are as common as positive ones.
Prior to the demonstration seen in this video, lights were placed along the track to show the position of the rolling ball at one-second intervals; the lights flash simultaneously, once per second, and are aligned such that the ball is directly above a light as they flash.
Academic standards correlations on Teachers' Domain use the Achievement Standards Network (ASN) database of state and national standards, provided to NSDL projects courtesy of JES & Co.
We assign reference terms to each statement within a standards document and to each media resource, and correlations are based upon matches of these terms for a given grade band. If a particular standards document of interest to you is not displayed yet, it most likely has not yet been processed by ASN or by Teachers' Domain. We will be adding social studies and arts correlations over the coming year, and also will be increasing the specificity of alignment.