# What is the speed of an object that travels from ( -9,0,1)  to ( -1,4,3 )  over 2 s?

Apr 19, 2016

speed: $\sqrt{21} \text{units"/"sec" ~~4.58 "units"/"sec}$

#### Explanation:

Distance between $\left(- 9 , 0 , 1\right)$ and $\left(- 1 , 4 , 3\right)$
is
$\textcolor{w h i t e}{\text{XXX}} d = \sqrt{{\left(- 1 - \left(- 9\right)\right)}^{2} + {\left(4 - 0\right)}^{2} + {\left(3 - 1\right)}^{2}}$
$\textcolor{w h i t e}{\text{XXXx}} = \sqrt{{8}^{2} + {4}^{2} + {2}^{2}}$
$\textcolor{w h i t e}{\text{XXXx}} = \sqrt{64 + 16 + 4}$
$\textcolor{w h i t e}{\text{XXXx}} = \sqrt{84}$
$\textcolor{w h i t e}{\text{XXXx}} = 2 \sqrt{21}$ (units)

Assuming a constant speed, $s$
color(white)("XXX")"speed" = "distance"/"time"
So
$\textcolor{w h i t e}{\text{XXX")s=(2sqrt(21) " units")/(2 " sec}}$

color(white)("XXX")=sqrt(21) "units"/"sec"

$\textcolor{w h i t e}{\text{XXX}} \sqrt{21} \approx 4.58$ (using a calculator)