# Vectors and the Kinematic Variables

Vectors have magnitude AND position.

Variables that just have a magnitude are called scalar quantities.

Vectors can be denoted by a little arrow over their variable names, or by being written in boldface.

If we look at position as a function of time, the change in the position has a direction and magnitude, and thus can be considered a vector. This is called displacement.

x(t) = position as a function of time

∆ x = xf - xi = displacement. Units are the units of distance (m)

The change in the displacement with respect to time is a vector called velocity. The magnitude of the velocity is called speed.

Units of velocity are units of speed (distance/time → m/s)

The change in the velocity with respect to time is a vector called acceleration.

Units of acceleration are (speed/time → m/s2)

## The kinematics equations

“Name” of equation | |||

VAX | vf2 = | vo2 | + 2a ∆ x |

VAT | vf = | vo | + at |

XAT | ∆ x = | vot | + ½ at2 |

*Things to note about the above equations:

- The names help you memorize them. The first letter is the term on the left. The last two letters describe the second term. The first term is always a “vo” term. The units of the right-sided terms are always the same as the left-sided ones.

- VAX is the only equation which doesn’t use time. Use it when you don’t know time.

A link to a page which goes through the derivation of these equations (note than on that webpage, they use the variable name “s” for displacement instead of ∆ x: