# GeoGebra

## Equation of Motion App

Access the app in full screen here: https://www.geogebra.org/m/mfvvhjrj

This app is designed to give students practice in interpreting velocity-time graphs with various scenarios, such as more complex examples involving negative velocity and acceleration. Answers will be given if student is wrong.

Use this to embed into SLS or another LMS.

<iframe scrolling="no" title="Equations of Motion" src="https://www.geogebra.org/material/iframe/id/mfvvhjrj/width/700/height/480/border/888888/sfsb/true/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/false/rc/false/ld/false/sdz/false/ctl/false" width="700px" height="480px" style="border:0px;"> </iframe>

## Root-mean-square Currents

The concept of root-mean-square values for Alternating Currents is challenging if students are to relate the I-t graph with the Irms value directly.

They have to be brought through the 3 steps before arriving at the Irms value. This interactive applet allows them to go through step by step and compare several graphs at one time to see the relationship.

Through the interaction, students might be asked to observe that the Irms value is never higher than the peak Io.

For a complete sinusoidal current:

For a diode-rectified current:

In comparing the Irms of both currents, students can be asked to consider why the ratio of the values is not 2:1 or any other value, from energy considerations.

Worked on this earlier as I am the lead lecturer for this JC2 topic and am trying to integrate useful elements of blended learning. Do let me know in the comments if you have ideas or feedback that you would like to share.

## Pressure-Distance Graph of a Sound Wave

This GeoGebra applet was modified from an existing applet to show the relationship between the pressure-distance and displacement-distance graph of a progressive longitudinal wave.

## Escape Velocity

Using the GeoGebra app above, I intend to demonstrate the relationship between total energy, kinetic energy and gravitational potential energy in a rocket trying to escape a planet’s gravitational field.

By changing the total energy of the rocket, you will increase the initial kinetic energy, thus allowing it to fly further from the surface of the planet. The furthest point to which the rocket can fly can be observed by moving the slider for “distance”. You will notice that the furthest point is where kinetic energy would have depleted.

Gravitational potential energy of an object is taken as zero at an infinite distance away from the source of the gravitational field. This means gravitational potential energy anywhere else takes on a negative value of $\dfrac{-GMm}{r}$. Therefore, the total energy of the object may be negative, even after taking into account its positive kinetic energy as total energy = kinetic energy + gravitational potential energy.

The minimum total energy needed for the rocket to leave the planet’s gravitational field is zero, as that will mean that the minimum initial kinetic energy will be equal to the increase in gravitational potential energy needed, according to the equation $\Delta U = 0 – (-\dfrac{GMm}{R_P})$, where $R_P$ is the radius of the planet.

Since $\dfrac{1}{2}mv^2 = \dfrac{GMm}{R_P}$, escape velocity, $v = \sqrt{\dfrac{2GM}{R_P}}$.

## Template for self-assessment questions

Here is a template that I might use to generate questions for students’ self-assessment in future. Based on a query that one of the participants in a GeoGebra online tutorial asked about generating random questions for simple multiplication for lower primary students.

The online tutorial was conducted by some teachers in the Singapore MOE GeoGebra community to share how GeoGebra could be used to create resources for home-based learning.