Relationship between displacement-time and velocity-time graphs

Through this GeoGebra app, students can observe how the gradient of the displacement-time graph gives the instantaneous velocity and how the area under the velocity-time graph gives the change in displacement.

In the GeoGebra app below, you will see a displacement-time graph on the left and its corresponding velocity-time graph on the right. These graphs will be referring to the same motion occuring in a straight line. Instructions

  1. Click "Play" and observe the values of displacement and velocity change in each graph over time.
  2. Note the relationship between the gradient in the displacement-time graph and the value of velocity.
  3. Note the relationship between the area under the velocity-time graph and the value of displacement.

Work Done Simulation

This GeoGebra app allows users to change the magnitude and direction of the force acting on an object, as well as the initial velocity.

The change in kinetic energy is calculated along with the work done in the direction of the force.

This demonstrates a very important concept in Physics known as the Work-Energy Theorem, where the net work done on a particle equals to its change in kinetic energy.

Does Hydrostatic Pressure Depend on Container Shape?

The following GeoGebra app simulates a pressure sensor that measures hydrostatic pressure, calibrated to eliminate the value of atmospheric pressure.

The purpose of this simulation is to address certain misconceptions by students such as the assumption that the shape of a container affects the pressure such that the pressure differs in different containers when measured at the same depth.

Drag the dot around to compare the pressure values at the same height between both containers.

The following codes can be used to embed this into SLS.

<iframe scrolling="no" title="Hydrostatic Pressure" src="https://www.geogebra.org/material/iframe/id/wbjduxt7/width/640/height/480/border/888888/sfsb/true/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/true/rc/false/ld/false/sdz/false/ctl/false" width="640px" height="480px" style="border:0px;"> </iframe>

Hydrostatic Pressure and Upthrust

This app is used to demonstrate how a spherical object with a finite volume immersed in a fluid experiences an upthrust due to the differences in pressure around it.

Given that the centre of mass remains in the same position within the fluid, as the radius increases, the pressure due to the fluid above the object decreases while the pressure below increases. This is because hydrostatic pressure at a point is proportional to the height of the fluid above it.

It can also be used to show that when the volume becomes infinitesimal, the pressure acting in all directions is equal.

The following codes can be used to embed this into SLS.

<iframe scrolling="no" title="Hydrostatic Pressure and Upthrust" src="https://www.geogebra.org/material/iframe/id/xxeyzkqq/width/640/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="640px" height="480px" style="border:0px;"> </iframe>

IP3-02-Kinematics

Graphical relationship between acceleration, velocity and displacement

I created the following GeoGebra app to illustrate the relationships between the physical quantities acceleration, velocity and displacement.

  1. Modify the acceleration graph using the two green dots. Notice how the velocity and displacement graphs would change.
  2. You can set the initial values of velocity and displacement using the orange and red dots respectively.
  3. Press "Play" to observe how the object moves. Note: the animation takes place in slow-motion, not in real time.
  4. Uncheck any of the graphs to hide them.

Here are some learning activities you can try out.

  1. Predict the displacement-time graph, following these steps:
    1. Uncheck the displacement-time graph.
    2. Move the two dots on the acceleration-time graph to zero acceleration.
    3. Move the initial velocity to - 10 m s-1.
    4. Predict how the displacement-time graph will look like.
  2. Predict/describe the movement of the object.
    1. Set the dots for acceleration to remain constant for a period of 4 seconds at - 10 m s-2, initial velocity at 20 m s-1, and initial displacement at 0 m.
    2. Predict how the object will move, taking the upward direction as positive.
    3. Press "Play" to verify your answers.

For embedding into SLS:

<iframe scrolling="no" title="Acceleration, velocity and displacement graphs" src="https://www.geogebra.org/material/iframe/id/qpxcs6vb/width/638/height/478/border/888888/sfsb/true/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/true/rc/false/ld/false/sdz/false/ctl/false" width="638px" height="478px" style="border:0px;"> </iframe>

Area under velocity-time graph