# What is the speed of an object that travels from ( -5 , 2, -8)  to (6 , -2, 7 )  over 4 s?

Feb 22, 2016

$v \cong 4 , 76 \frac{m}{s}$

#### Explanation:

${P}_{1} = \left({x}_{1} , {y}_{1} , {z}_{1}\right)$
${P}_{2} = \left({x}_{2} , {y}_{2} , {z}_{2}\right)$
$\Delta x = {x}_{2} - {x}_{1}$
$\Delta y = {y}_{2} - {y}_{1}$
$\Delta z = {z}_{2} - {z}_{1}$
$\text{distance between two points is given by:}$
$\Delta s = \sqrt{\Delta {x}^{2} + \Delta {y}^{2} + \Delta {z}^{2}}$
$\Delta s = \sqrt{{11}^{2} + {\left(- 4\right)}^{2} + {15}^{2}} = \sqrt{121 + 16 + 225}$
$\Delta s = \sqrt{362}$
$\Delta s \cong 19 , 03 m$
$v = \frac{\Delta s}{\Delta t}$
$v = \frac{19 , 03}{4}$
$v \cong 4 , 76 \frac{m}{s}$