Mechanics is the study of the way objects move and interact, of forces and their effects. Historically the unravelling of the laws of mechanics took a long time, developing a considerable time after a lot of other mathematics had been worked out. The Greeks for example thought that a ball thrown through the air was kept moving by the rushing of the air behind it. It was not until nearly 2000 years afterwards when Galileo and Newton applied scientific methods to the subject in the seventeenth century that our current understanding began to emerge.
Newton was able to identify three fundamental laws that allow us to determine mechanical activity in bodies ranging in size from molecules to galaxies. NASA needs only these laws to calculate the movement of interplanetary probes. Since Einstein there have been extensions to deal with the very small scale and very high velocities but Newtonian Mechanics is still adequate for everyday experience.
One simple case study in mechanics is the motion of a body moving under gravity because we have a limited number of forces acting.
Looking at projectile motion
There is something common to the movement of all objects in projectile motion.
The images below are frames from video clips of a variety of different objects in motion. Can you predict the path they will take? Where do you expect the objects to land? Why is it important to be able to predict where the objects will land? How would you describe the common factor?
Do you know what algebraic equation would have a graph of this shape?