Scalars, vectors, and one dimensional motion

In this lesson, we will learn:

• Definition of scalar and vector
• How to write scalars and vectors in physics
• The definitions of distance, displacement, speed, and velocity
• Calculations involving scalars and vectors

• Scaler: a quantity with a magnitude only

• Vector:a quantity with magnitude and direction

• Symbols for vectors can be written with arrows on top (like $\vec{d}$), symbols for scalars do not have arrows (like t)
• Distance, speed, time, and mass are examples of scalars: they do not have a direction.
• Position, displacement, and velocity are examples of vectors: they do have direction.

Displacement

$\Delta \vec{d}$: $\vec{d}_f - \vec{d}_i$

$\Delta \vec{d}: \mathrm{displacement, \;in\;meters\;(m)}$

$\vec{d}_f: \mathrm{final\;position, \;in\;meters\;(m)}$

$\vec{d}_i: \mathrm{initial\;position,\;in\;meters\;(m)}$

Speed

$v = d/t$

$v:\mathrm{speed, \;in \;meters \;per \;second \;(m/s)}$

$d:\mathrm{distance, \;in \;meters \;(m)}$

$t:\mathrm{time \;interval, \;in \;seconds \;(s)}$

Velocity

$\vec{v} = \Delta \vec{d}/t$

$\vec{v}: \mathrm{velocity,\;in\;meters\;per\;second\;(m/s)}$