A stock undergoes acceleration if it is acted upon by another stock, by itself, or by an exogenous cause.

Consider the case where a stock *x* is influenced by another stock *y*. *x* and *y* can represent any variables, such as population numbers or social variables. The system dynamics diagram and differential equation are:

where* b* is a constant.

Changes in *y* are reflected in changes in *x*, i.e. *y* is the cause of changes in *x*’s behaviour. This can be interpreted as *y* exerting a force on *x* as changes in *y* cause *x* to accelerate. Differentiate the equation:

If *y* is changing, non-zero derivative, then *x* accelerates. The influence from *y* causes *x*’s behaviour to deviate from uniform motion, the classic Newtonian definition of force. The value of the force is *F* = d*y*/d*t*.

The parameter *b* governs the response of *x* to *y*. The larger the value of *b* the more *x* responds to *y*. Thus *b* is the equivalent of the inverse of the mass, *b* = 1/*m*, as a lighter stock *x* responds more to a given force. Thus:

is the equivalent of Newton’s second law of motion for system dynamics. The mass of the stock m converts the force from y into acceleration of *x*.

### Constant Force

Let the rate of change of *y*, its flow, be constant *k*:

Then the change in *y* causes *x*’s behaviour to deviate from a straight line, i.e. *y* induces

acceleration in *x*:

Mathematically:

Thus *x* is quadratic and its graph over time is curved.

If *y* is constant then *k* = 0 and thus *x* changes linearly, uniform motion. This is the system dynamics equivalent of Newton’s first law of motion. In this case a stock will remain constant, or change uniformly, unless acted upon by a force from another stock, itself, or an exogenous cause.

The impact of the constant force of *y* on *x* is:

Impact is a ratio measure of force, the acceleration of *x* imparted by *y* divided by the rate of change of *x*. It is also the force from *y* divided by the momentum of *x*. In the case of a constant force, the impact of *y* is decreasing with time, showing that a constant force has diminishing effect on stock as it increases, i.e. the time graph of the stock is becoming less curved.