# What is the speed of an object that travels from ( 8 , -3, 6 )  to ( -8 , -4 ,1 )  over 2 s?

Jul 24, 2018

Speed of object is about $8.4$ units per second

#### Explanation:

The distance between two points $\left({x}_{1} , {y}_{1} , {z}_{1}\right)$ and $\left({x}_{2} , {y}_{2} , {z}_{2}\right)$ is given by

$\sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2} + {\left({z}_{2} - {z}_{1}\right)}^{2}}$

Hence distance between $\left(8 , - 3 , 6\right)$ and $\left(- 8 , - 4 , 1\right)$ is

$\sqrt{{\left(- 8 - 8\right)}^{2} + {\left(- 4 - \left(- 3\right)\right)}^{2} + {\left(1 - 6\right)}^{2}}$

= $\sqrt{{\left(- 16\right)}^{2} + {\left(- 1\right)}^{2} + {\left(- 5\right)}^{2}}$

= $\sqrt{256 + 1 + 25}$

= $\sqrt{282}$

= $16.793$

As a distance of $16.793$ is covered in $2 s$

speed of object is $16.793 = 8.397 \cong 8.4$ per second