# Scalars, vectors, and one dimensional motion

##### Intros

###### Lessons

##### Examples

###### Lessons

**Distance and displacement, speed and velocity**

Betty walks 5 m to the east, then 7 m to the west, in 10 s.

- What is the total distance travelled?
- What are Betty's initial and final positions, and displacement?
- What is Betty's speed?
- What is Betty's velocity?

**Rearranging $\vec{v} = \Delta\vec{d}/t$ for displacement and time**

A car travels at 11.0 m/s [E]

- What is its displacement if it travels for 13.5 s?
- How long does it take to travel 542 m?

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###### Topic Notes

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**

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

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

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