## 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.

## Instantaneous vs Average Velocity

This GeoGebra app allows students to observe the difference between instantaneous and average velocity from a graphical perspective.

## 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.
``<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>``