Engineering topics: Position, Velocity, Acceleration

I got my bachelor’s degree in chemical engineering, and graduated in 2011. Since then, I haven’t had the chance to do much actual engineering (an odd side effect of having “engineering” positions is that they don’t involve using any of the technical knowledge I gained in school!), but I still enjoy learning and talking about the topic. One of my favorite classes in engineering was phyics – specifically, calculus-based physics of mechanics and motion. It always made a lot of sense to me, intuitively, and I had fun tutoring my classmates in these topics as well. I rather miss the teaching part of being in school, actually: I found it helped me learn the subjects a lot more thoroughly as well.

One of the first concepts we learn about in physics is the idea of position, velocity, and acceleration. Here are the basics:


Position – where an object is with respect to time: x(t). “t” is time, “x” is position. When using this notation, you need to set a point in space as position “0”, your start point. It doesn’t actually matter where you set this point, as long as you stay consistent throughout the calculation. For example, here’s a graph of the position of an object thrown straight up in the air. It goes up, achieves a maximum height, then falls back down. In this case it’s only traveling vertically, so we can use one graph for position since its horizontal position doesn’t change.


Velocity – not quite an object’s speed! Speed and velocity are two different terms, scientifically speaking. Speed denotes how quickly an object’s position is changing with respect to time, while velocity denotes both the object’s speed and its direction. So, velocity can be negative. As with position, denoting velocity as v(t) requires you to set one direction as positive and the other direction as negative. We’re assuming the object is traveling in one dimension here – in this case, the object is going either straight up or straight down. So, we can set “up” as positive velocity, and “down” as negative velocity. Here’s the graph of the thrown object’s velocity as it is thrown. Notice that while the graph of position formed a curved line heading up and down, this graph forms two straight lines.


This is because velocity is the derivative, or slope, of position. Looking at the graph of position, one can see that the slope of the curve starts out high, then decreases to zero as the object hits its maximum height, then starts increasing again as the object falls, but now it’s a negative number. It’s a straight line from a positive number to the equivalent negative number. Velocity can be found directly from position.

Acceleration – how quickly an object’s velocity is changing over time: a(t). It’s the force that pushes you back in your seat in a fast car: the faster a car accelerates, the more quickly its speed can go from 0 to 60 mph. Positive acceleration means an object’s velocity is increasing, while negative acceleration means its velocity is decreasing. Notice that velocity can decrease and go negative! In the case of the object thrown straight up, this means the object is heading downward and speeding up. Here’s the graph of the object’s acceleration with respect to time:


Here’s something interesting. Again, acceleration is found as the slope of velocity. Since the graph of velocity was a straight line, its slope is actually constant: -9.8 m/s², the acceleration due to gravity. When the object is thrown, gravity is the only force acting on it, constantly pulling it back to earth. So as it travels upward, it slows down, stops briefly at the top of its arc, and then speeds up as it heads back down again.


These are the basics of motion in physics. The topic can be made more complicated: continuing to take the slope of acceleration can give a term known as jerk, which is how quickly acceleration is changing. In the case of the thrown object, acceleration isn’t changing, so jerk would be 0. The term can be used in other situations, such as when measuring discomfort to passengers in a vehicle. High jerk causes discomfort, so this measurement can be tracked and limited.

After that it gets a bit weird. Proposed measurements for measuring subsequent slopes have been called snap (rate of change of jerk), crackle (rate of change of snap), and pop (rate of change of crackle)! These aren’t widely accepted measurements, however, and examples like this show that every once in a while scientists do actually exhibit a sense of humor…

So, am I alone in having a favorite physics topic? Feel free to send suggestions on what to talk about!


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