Understanding motion in physics often involves analyzing displacement, velocity, and acceleration graphs. With the interactive GeoGebra graph at this link, you can dynamically explore how these concepts are connected.
How It Works
This interactive simulation lets you visualize an object’s motion and its corresponding displacement-time, velocity-time, and acceleration-time graphs. You can interact with the model in two key ways:
Adjust Initial Conditions:
Move the dots on the graph to change the starting displacement, velocity, or acceleration.
Observe how these changes influence the overall motion of the object.
Use the Slider to Animate Motion:
Slide through time to see how the object moves along its path.
Watch the displacement vector, velocity vector, and acceleration vector update in real time.
Key Observations
When displacement changes, the velocity and acceleration graphs adjust accordingly.
A constant acceleration results in a straight-line velocity graph and a quadratic displacement graph.
Negative acceleration (deceleration) slows the object down and can cause direction reversals.
If velocity is constant, the displacement graph is linear, and acceleration remains at zero.
Why This is Useful
This GeoGebra tool is perfect for students and educators looking to build intuition about kinematics. Instead of just solving equations, you get a visual and hands-on way to see the relationships between these key motion variables.
Try it out yourself and experiment with different conditions to deepen your understanding of motion!
This week, I conducted a lesson on motion for my IP3 class using a simple yet effective tool: a simulated ticker tape timer. The objective was to help students develop an intuitive understanding of uniform and non-uniform motion by actively engaging in an experiment.
Introduction to the Ticker Tape Timer
To kickstart the lesson, I showed my students a YouTube video that explains how a ticker tape timer works:
This video provided a visual demonstration of how a ticker tape timer marks regular intervals on a moving strip of paper, allowing us to analyze motion quantitatively.
Hands-On Experiment: Simulating a Ticker Tape Timer
After the video, I had students pair up for a hands-on activity. Instead of using an actual ticker tape timer, we simulated the process using paper strips cut from A3-sized sheets. Each pair had one student act as the “moving arm,” responsible for placing dots on the strip, while the other played the role of the “puller,” responsible for pulling the paper strip at different speeds.
To ensure a consistent time interval between each dot, I used a Metronome App that I created:
This app produces a steady rhythm at 120 beats per minute, meaning that the interval between each beep (and consequently each dot) is 0.5 seconds. To improve accuracy, the student acting as the moving arm was instructed to close their eyes and focus solely on the beep.
Step 1: Recording Uniform Motion
In the first trial, the puller was asked to pull the paper at a constant rate. As the paper moved steadily, the moving arm marked dots at regular intervals based on the metronome beat. After completing the trial, students used a ruler to measure the distances between successive dots. Since the time interval was fixed, they could easily calculate the speed of the paper by using:
Step 2: Recording Accelerated Motion
Next, the students switched roles. This time, the new puller was asked to gradually increase the speed of the paper. As expected, the spacing between dots increased progressively, providing a clear visual representation of acceleration. This led to discussions on how motion can be analyzed using dot patterns and how acceleration differs from uniform motion.
Reflections and Key Takeaways
This activity was highly effective in reinforcing key motion concepts. Since we do not have an actual ticker tape machine, it allowed students to engage in a hands-on simulation while visually and physically experience motion rather than just reading about it.
Next Steps
To extend this lesson, I plan to introduce velocity-time graphs and have students plot their measured speeds to analyze changes in motion further. Additionally, incorporating digital tools like video analysis with Tracker software could help reinforce these concepts further.
If you have any feedback or suggestions, feel free to share them in the comments below!
This deck of slides are the ones I will be using for the Symposium on “Leveraging Technology for Engaging and Effective Learning” at the Singapore International Science Teachers’ Conference (SISTC) 2024 on Day 2 of the Conference (20 November). Feel free to download for your reference.
In recent years, AI tools like DALL-E and MidJourney have gained popularity for generating stunning, artistic images. However, when it comes to creating scientific illustrations, particularly for exams, we need accuracy, clarity, and precision. This is where LaTeX, a document preparation system widely used in academia, shines. Combined with the intelligence of ChatGPT, LaTeX can produce exactly the images you need without the artistic flair or ambiguity that tools like DALL-E might introduce.
The process of generating science exam images using ChatGPT and LaTeX is straightforward:
Describe the Diagram: You begin by providing a detailed description of the diagram or scientific illustration you need. For example, “Generate a diagram using Latex showing a free-body diagram of a block on an inclined plane with friction.”
ChatGPT Generates LaTeX Code: Based on your description, ChatGPT can generate the appropriate LaTeX code, using packages like TikZ or PGFPlots to create the required scientific diagram. The output might look like this: \documentclass{standalone} \usepackage{tikz} \begin{document} \begin{tikzpicture} % Inclined plane \draw[thick] (0,0) -- (4,2); \draw[thick] (0,0) -- (4,0); % Block \draw[fill=gray] (2,1) rectangle (2.5,1.5); % Forces \draw[->,thick] (2.25,1.25) -- (2.25,2.25) node[above] {Normal Force}; \draw[->,thick] (2.25,1.25) -- (2.25,0.25) node[below] {Weight}; \draw[->,thick] (2.25,1.25) -- (3.25,1.25) node[right] {Friction}; \end{tikzpicture} \end{document}
Compile the LaTeX Code: Once the code is generated, you can compile it using any LaTeX editor (such as Overleaf or a local LaTeX distribution).
Check for Errors: The diagram is unlikely to look perfect in the first iteration. For example, the above code gives the following:
Edit: You can either instruct ChatGPT to modify specific sections of the diagram or make the changes yourself. After 3 more iterations, for example, ChatGPT produced the following codes: \begin{tikzpicture} % Inclined plane \draw[thick] (0,0) -- (4,2); \draw[thick] (0,0) -- (4,0); % Block (rotated to match the slope) \draw[fill=gray, rotate around={26.565:(2.25,1.25)}] (2,1) rectangle (2.5,1.5); % Forces (adjusted for friction up the slope) % Normal Force (perpendicular to the slope) \draw[->,thick] (2.25,1.25) -- ++(-0.447,0.894) node[above left] {Normal Force}; % Weight (straight down) \draw[->,thick] (2.25,1.25) -- (2.25,0.25) node[below] {Weight}; % Friction (along the slope, now pointing up the incline) \draw[->,thick] (2.25,1.25) -- ++(0.894,0.447) node[above right] {Friction}; \end{tikzpicture}
This is the output image:
Integrate into Teaching Materials: Once you are satisfied with the output, the compiled image can then be saved as a PDF, PNG, or any other image format and directly embedded into your exam materials.
The following are similar images made using the same workflow and their corresponding codes, which I made changes to manually instead as it was faster for me once I became familiar with the coordinate-system based drawing method.
When applying the principle of moments to calculate the magnitude of a force creating a turning effect, where the force is not perpendicular to the length of the object, there are two approaches.
Take the following problem:
A uniform rectangular beam has negligible thickness and weight 850 N. Its length is 5.0 m and it is in contact with the top of a support at point P. P is 0.80 m from one end of the beam.
The beam is held stationary, at an angle of 30° to the horizontal, by a rope that is attached to the bottom corner of the other end of the beam.
Calculate the magnitude of the force T on the beam due to the tension in the rope.
Approach 1: Identifying the perpendicular distance between line of action of the force and pivot
In the applet above, check the box that says “Show perp dist” to see the lines representing the perpendicular distances between each line of action of the force and the pivot P.
Taking moments about P,
Clockwise moment due to T = Anti-clockwise moment due to W
The simulation below allows students to practise calculating potential differences and currents of a slightly complex circuit, involving three different modes that can be toggled by clicking on the switch.
When resistors \( R_1 \) and \( R_2 \) are connected in series, the total resistance is simply the sum of the individual resistances:
\[ R_{\text{total}} = R_1 + R_2 \]
The current \( I \) through the circuit is given by Ohm’s Law:
\[ I = \frac{V_{\text{total}}}{R_{\text{total}}} = \frac{V_{\text{total}}}{R_1 + R_2} \]
where \( V_{\text{total}} \) is the total potential difference supplied by the source.
The potential difference across each resistor can be calculated using:
\[ V_1 = I \cdot R_1, \quad V_2 = I \cdot R_2 \]
Mode 2: \( R_1 \) and \( R_3 \) in Parallel, \( R_2 \) in Series
In this mode, resistors \( R_1 \) and \( R_3 \) are in parallel, and \( R_2 \) is in series with the combination. First, calculate the equivalent resistance of the parallel combination:
Mode 3: \( R_1 \) and \( R_2 \) in Series, \( R_3 \) in Parallel
Here, resistors \( R_1 \) and \( R_2 \) are connected in series, and the combination is in parallel with \( R_3 \). First, calculate the resistance of the series combination:
\[ R_{\text{series}} = R_1 + R_2 \]
Then, find the total resistance of the parallel combination: