Mechanics is more than just an application of algebra and
geometry, it is *the* *primary *application of geometry and
algebra. Newton’s development of
calculus was to answer problems in what we would now call mechanics and much of
his work was geometrical in nature.
However, students study less geometry than they use to and this, along
with difficulties in algebra, can result in issues when they start studying
mechanics.

As a remedy to this software that links geometry and algebra
is perfect tool in which students can practise modelling situations in
mechanics. This can complement their
studies in mechanics and enhance their skills.

In particular two main methods that lend themselves well to
being represented in software are interactive force diagrams and animations of
position.

##
Interactive force diagrams

Interactive force diagrams can be created where the vectors
for the forces acting on an object are represented dynamically.

The diagram below shows the forces acting on a block when
there is a pulling force at some angle to the upwards vertical.

##
Animations of position

Many other situations in mechanics are about describing how
objects move and this movement is often defined as function as time. This may be something as straightforward as
the position being given as a linear function of the time (in the case of
constant velocity) or more completed examples where the velocity, acceleration
or force are given as functions of the time.

Most graph-plotters and dynamic geometry software allow for
a function, or the coordinates of a point, to be defined in terms of a
parameter, t. This means that if you
know the x and y-position of a particle as a function of the time these can be
entered to give the path of the particle.

To further enhance this a slider can be added for t and the both
the position of the particle and vectors for velocity (and acceleration) can be
shown. In Geogebra once a slider has
been added this can be animated.

The example below shows the position, velocity and speed for
a particle where these are functions of time.

##
Further examples