Mathematics of Movement

Work

In physics, Work is not a place we go to get a paycheck. It is something we do all the time, whether we are at our employment, making a meal, sleeping, etc. Mathematically, Work is defined as

Work = Force × Displacement

W=FD

Work is measured in joules (J), which is the amount of work performed when 1 Newton (N) of Force changes an object’s position by one meter.

Force as a Component of Work

Force is additionally defined as

Force = mass × acceleration

F = ma

, where mass is measured in kilograms and acceleration is measured in meters / second.

Acceleration in Force

Acceleration can be simplified to velocity (v) and time (t).

Force = mass × Δv / Δt

“Δ” represents the quantity Delta, the mathematical word for “rate of change”, so Acceleration is defined as the rate at which an object’s velocity changes over time.

Velocity changes its rate when an object speeds up, slows down, or changes its direction. These qualities make Acceleration an extremely dynamic variable because there is no setpoint for Acceleration in movement.

Time in Acceleration

The reason Acceleration has no kinetic set point is because it contains an element of time. The addition of time to any physical equation introduces the potential for efficiency to be lower or higher as a function of hierarchical decision-making in any physical action.

In a phrase, for any action we take, we can make decisions to do it inefficiently and poorly, or efficiently and well.

More Information on the Mathematics of Movement

Displacement in Work