# Scalars, vectors, and one dimensional motion

### Scalars, vectors, and one dimensional motion

#### Lessons

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

Notes:

• 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

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

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

• Introduction
Introduction to scalars, vectors, and one dimensional motion
a)
How to write scalars and vectors; definitions of distance, position and displacement

b)
Definitions of speed and velocity

• 1.
Distance and displacement, speed and velocity
Betty walks 5 m to the east, then 7 m to the west, in 10 s.
1. What is the total distance travelled?
2. What are Betty's initial and final positions, and displacement?
3. What is Betty's speed?
4. What is Betty's velocity?

• 2.
Rearranging $\vec{v} = \Delta\vec{d}/t$ for displacement and time
A car travels at 11.0 m/s [E]
1. What is its displacement if it travels for 13.5 s?
2. How long does it take to travel 542 m?