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

Jun 19, 2016

The distance between points $\left({x}_{1} , {y}_{1} , {z}_{1}\right)$ and $\left({x}_{2} , {y}_{2} , {z}_{2}\right)$ is given by $r = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2} + {\left({z}_{2} - {z}_{1}\right)}^{2}}$
$= \sqrt{{\left(- 2 - 8\right)}^{2} + {\left(- 1 - \left(- 4\right)\right)}^{2} + {\left(6 - 3\right)}^{2}} = \sqrt{100 + 9 + 9} = \sqrt{118} \approx 10.9$. Then $v = \frac{d}{t} = \frac{10.9}{4} = 2.7$ $m {s}^{-} 1$.