# What is the speed of an object that travels from ( 7,1,6 )  to ( 4,-3,7 )  over 2 s?

May 1, 2018

${\text{speed"=sqrt(26)/2~~2.55 " units}}^{-} 1$

#### Explanation:

Let.

$a = \left(7 , 1 , 6\right)$ and $b = \left(4 , - 3 , 7\right)$

Then:

$\boldsymbol{\vec{a b}} = b - a = \left(- 3 , - 4 , 1\right)$

We need to find the magnitude of this. This is given by the distance formula.

$| | \boldsymbol{a b} | | = \sqrt{{\left(- 3\right)}^{2} + {\left(- 4\right)}^{2} + {\left(1\right)}^{2}} = \sqrt{26}$

$\text{speed"="distance"/"time}$

${\text{speed"=sqrt(26)/2~~2.55 " units}}^{-} 1$