Quantifying the Motion of Objects

What’s the Big Idea‽

Motion. How do we measure it? As Chris Rybicki points out, why even bother measuring it? Well, Chris, it turns out measuring an object’s motion is well worth the effort—it forms the fundamentals of physics.

An object’s motion can basically be described using three terms: displacement, velocity, and acceleration. Displacement is defined as “an object’s overall change in position”, with respect to direction. Likewise, velocity is the overall change in position per unit of time, and acceleration, the overall change in position per square unit of time (The Physics Classroom). 

Procedure

To find out how objects move, we set up two meter sticks side by side and taped them to the floor. Then, we took a tumble buggy and a utility vehicle and performed a series of trials with them, which looked much like this:

For each of the two vehicles, we placed them just in front of the starting line and let them go. Then, using a stopwatch, we recorded the time in seconds it took them to reach 0.5 m, 1.0 m, and so on. This process was repeated three times for each vehicle, after which the data was averaged to reduce random error. Additionally, we attempted to perform the procedure as consistently as possible to minimize systematic error.

Lastly, the visual representation of our data. We compiled the data in one set of displacement vs. time graphs (unfortunately not using Graphical Analysis, due to a few technical issues). Then, using the formula for velocity, v = p/t, and the formula for acceleration, a = v/t, we generated two more sets of graphs.

Tumble Buggy Displacement over Time

Tumble Buggy Velocity over Time

Tumble Buggy Acceleration over Time

Utility Vehicle Displacement over Time

Utility Vehicle Velocity over Time

Utility Vehicle Acceleration over Time

Some notes about the graphs above—since we recorded data manually, there is a fair amount of random error. This is most apparent in the utility vehicle graphs where there’s some pretty strange-looking data. I think that a more precise method would prevent this in future labs. Additionally, the graph-making app that we used didn’t really cooperate with us with the third graph from the top—I think we’re pretty sorry we didn’t use Graphical Analysis.

Takeaways

Displacement, velocity, and acceleration are some of the core concepts of kinematics and their relationships are clear. Velocity is the change of displacement over a period of time just as acceleration is the change of velocity over a period of time. And this works for further derivatives—be they jerk, jounce (or snap), crackle, or pop (Reid).

How do the graphs above model motion? Any displacement vs. time graph (or one of its derivatives) for an object whose motion doesn’t change will be linear. For an object whose motion does change, the graph would have to be modeled by a different function. The slope of the graph shows the rate of change of an object’s motion at any given point. If the vehicles were towing or dragging another object, the slopes of the graphs would decrease due to an increase in friction.

That’s all for now—time to displace!