# What is the speed of an object that travels from ( -2, -5, 1 )  to ( -5 , -7, 4 )  over 2 s?

Jan 15, 2016

$\approx 2.345 \frac{u n i t s}{s}$

#### Explanation:

In a Cartesian coordinate system distance d between two points ${P}_{1} \left({x}_{1} , {y}_{1} , {z}_{1}\right)$ and${P}_{2} \left({x}_{2} , {y}_{2} , {z}_{2}\right)$ is given by the formula

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

Inserting given values (−2,−5,1) and (−5,−7,4) for the points ${P}_{1}$ and ${P}_{2}$

$d = \sqrt{{\left(- 5 - \left(- 2\right)\right)}^{2} + {\left(- 7 - \left(- 5\right)\right)}^{2} + {\left(4 - 1\right)}^{2}}$
$d = \sqrt{22}$
Now using the formula $s p e e d = \frac{\mathrm{di} s t a n c e}{t i m e}$
$d = \frac{\sqrt{22}}{2}$