Change in Velocity

When I write the Greek letter Δ (delta) in front of a variable, I am talking about the change in that variable, usually between some initial moment and some final moment. For instance,

Δ \vec{v}

is the change in velocity, and

Δ t

is the change in time. The change in a variable A is defined as

Δ A = A_{f} - A_{i}

where $A_{i}$ is the variable's value at the initial moment and $A_{f}$ is its value at the final moment. The change in $A$ is also the value you need to add to the initial value to get the final value:

A_{f} = A_{i} + Δ A

The change in a vector quantity, like velocity, works exactly the same way: $Δ \vec{v} = {\vec{v}}_{f} - {\vec{v}}_{i} = {\vec{v}}_{f} + (- {\vec{v}}_{i})$

Column

Consider this motion diagram.

Column

To calculate the change in velocity, we take the negative of

{\vec{v}}_{i}

and add it to

{\vec{v}}_{f}

, to get

Δ \vec{v}

${\vec{v}}_{f} + (- {\vec{v}}_{i}) = Δ v$

Column

We can also think of

Δ v

as what we add to

{\vec{v}}_{i}

to get

{\vec{v}}_{f}

${\vec{v}}_{f} = {\vec{v}}_{i} + Δ \vec{v}$

Note

Remember that the displacement is written as $Δ \vec{x}$ ? While it is easiest to think of it as the vector from one spot to another, we can think of it as a "change of position". To do that, we define the position vector of a spot as the vector from the origin to that spot.