# What is the speed of an object that travels from ( 8,-8,2)  to ( -5 , -3,-7 )  over 2 s?

Feb 5, 2016

$v = 8 , 2925$

#### Explanation:

${P}_{1} : \left(8 , - 8 , 2\right) \text{ point of starting}$
${P}_{2} : \left(- 5 , - 3 , - 7\right) \text{ point of ending}$
$\Delta x = {P}_{2 x} - {P}_{1 x} = - 5 - 8 = - 13$
$\Delta y = {P}_{2 y} - {P}_{1 y} = - 3 + 8 = 5$
$\Delta z = {P}_{2 z} - {P}_{1 z} = - 7 - 2 = - 9$
$\text{distance between two point is given by:}$
$s = {\left(\Delta {x}_{x}^{2} + {\Delta}_{y}^{2} + {\Delta}_{z}^{2}\right)}^{\frac{1}{2}}$
$s = {\left(169 + 25 + 81\right)}^{\frac{1}{2}}$
$s = {\left(275\right)}^{\frac{1}{2}}$
$s = 16 , 585$
$s p e e d = \left(\text{distance")/("elapsed time}\right)$
$v = \frac{16 , 585}{2}$
$v = 8 , 2925$