As one of the first topics in A-level physics, kinematics introduces JC students to the variation of velocity and displacement with acceleration. Very often, they struggle with the graphical representations of the 3 variables. This Geogebra app allows students to vary acceleration (keeping it to a linear function for simplicity) while observing changes to velocity and displacement. Students can also change the initial conditions of velocity and displacement. The default setting shows an object being thrown upwards with downward gravitational acceleration of 10 m s^-2. The movement of the particle with time is shown on the left with a reference line showing the position on the displacement graph. GeoGebra link: https://www.geogebra.org/m/qpxcs6vb

GeoGebra link: https://www.geogebra.org/m/hzfyjejx GeoGebra link: https://www.geogebra.org/m/jmqytcsc

In order to help students visualise a wavefront, a 3-D image is usually used to show the imaginary line joining particles in phase. I created the GeoGebra apps below to allow students to change the wavefront and observe it move with time at a constant wave speed. There represent simplified versions of waves on a ripple tank with a linear and circular wavefront.

Linear Wavefront

A wavefront for a linear wave is a straight line that represents points of equal phase, typically generated by a plane wave source. These wavefronts are parallel to each other and move in a uniform direction as the wave propagates.

GeoGebra link: https://www.geogebra.org/m/rbjcszuc

Rotating the first waveform, you can get the displacement-distance profile of a wave, which is basically the cross-section of a 3-D wave.

Circular Wavefront

A wavefront for a circular wave is a continuous line or curve that represents points of equal phase, emanating outward from a central source. In a two-dimensional medium, these wavefronts are concentric circles that expand as the wave propagates away from the source.

GeoGebra link: https://www.geogebra.org/m/axdhtccg

GeoGebra link: https://www.geogebra.org/m/f7faw3r6 This simple Geogebra app allows students to observe the oscillation of a particle perpendicular to the direction of energy transfer.

This Geogebra app allows students to explore how the position of the centre of gravity as well as the width of its base affect the stability of an object.