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

Jan 21, 2016

First of all let us find find the distance between the two given points.
The distance formula for Cartesian coordinates is

d=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2
Where ${x}_{1} , {y}_{1} , {z}_{1}$, and ${x}_{2} , {y}_{2} , {z}_{2}$ are the Cartesian coordinates of two points respectively.
Let $\left({x}_{1} , {y}_{1} , {z}_{1}\right)$ represent $\left(8 , 4 , 1\right)$ and $\left({x}_{2} , {y}_{2} , {z}_{2}\right)$ represent $\left(6 , - 1 , 6\right)$.
implies d=sqrt((6-8)^2+(-1-4)^2+(6-1)^2
implies d=sqrt((-2)^2+(-5)^2+(5)^2
implies d=sqrt(4+25+25
implies d=sqrt(54 units

Hence the distance is $\sqrt{54}$ units.

$S p e e d = \frac{D i s \tan c e}{T i m e}$

$S p e e d = \frac{\sqrt{54}}{4} = 1.837 \frac{u n i t s}{\sec}$

If the units is meter then
$S p e e d = 1.837 \frac{m}{s}$.