Delta means 'change in.'

Delta looks like this:

A complete explanation follows.

In this discussion, as it relates to kinematics and the study of physics in general, the Greek letter delta means 'change in.'

The Greek letter delta, when used this way,
** looks like** this:

It means ** 'change in'**. So, if the variable

is read
** 'change in position.'** It could also be read

If the variable ** v stands for velocity**, then the following notation stands for

And ** 'change in time'** would look like this:

Now, any time there is a change in a quantity that change is calculated by taking the later value for that quantity and subtracting from it the earlier value for that quantity. So, for example, if an object were
** first** at a position given by the

The ** first position** at 3 meters would be called

Therefore, we would say that the ** change in position** was equal to

Note that changes in a quantity can be negative. If an object
** begins** its movement at a

Our latest examples here have been with changes in position, but delta calculations proceed the same way with other quantities. Here's another example. If an object was moving with a
** velocity of 8.2 m/s originally** and then changed its

And, if an experiment **
started** when

One note about the calculation for delta time: Unless you are working on some special time reversal problem, which would be unusual, but perhaps interesting; if you end up with a negative change in time, and you are working in classical Newtonian physics, then very most likely you have made a mistake.

So, in general, all delta quantity calculations proceed the same way.
** Take the later quantity and subtract from it the former quantity.** Here, we show the calculation with an abstract quantity, 'it'.

Hopefully, even if you are unsure regarding the meaning of the following symbols, the delta calculations make sense:

In calculus this way of thinking about the size of a change moves from an easily imagined size to a size of change so tiny it disappears. These types of changes are as tiny as infinity is large. They are called infinitesimals. |

In all of the above examples the ** subscript 1** and the

If we let the ** subscript 'o'** represent the

The above would be read: ** 'The change in position is equal to the final position minus the original position.'** Or, it could be read as:

Here is similar notation for a ** change in time**:

One can also use the ** subscript 'i'**, which means

This would be read: ** 'The change in time is equal to the final time minus the initial time'**,
or

Basically, '1' and '2' form one group of subscripts. Another group is 'f', 'o', and 'i'. One should
** not mix notation** from one group with another, as in:

Using position, or x, as an example, notice that by using algebra we can rearrange any of the above delta equations so that it solves for the first or the second value of the quantity. Specifically, if:

Then we can solve for x_{2}:

The above can be read:
** 'The second position equals the first position plus the change in position.'** But, in general, regarding a delta equation for any quantity, think of it this way:

And we can solve for x_{1}:

*This could be read:***
'The first position is equal to the second position minus the change in position.'** But, again, see this equation as it might apply to any quantity and also notice:

- The Greek letter delta, , means 'change in'.
- This 'change in' refers to a change in the value of some quantity.
- The change is calculated by subtracting the earlier value of the quantity from the later value of the quantity.
- This subtraction may yield a positive or a negative or zero change result.
- You can use the subscripts '1' and '2' to refer to the first and second values respectively.
- You can use the subscripts 'o', 'i', and 'f' also. The subscripts 'o' and 'i' mean original and initial respectively, and the subscript 'f' means final.

Also, closing note:

- The Greek letter delta can appear in other contexts and have other meanings. It can appear upper case or lower case, written as print or script. For example, lower case script delta is often used as a symbol for an angle, and in advanced calculus lower case script delta is used in the symbol for a partial derivative. But when delta is used as explained above, in upper case print, it always means 'change in'.