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

Jun 5, 2017

The speed is $= 2.32 m {s}^{-} 1$

#### Explanation:

The distance between the points $A = \left({x}_{A} , {y}_{A} , {z}_{A}\right)$ and the point $B = \left({x}_{B} , {y}_{B} , {z}_{B}\right)$ is

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

$\mathrm{dt} = \sqrt{{\left(- 1 - 6\right)}^{2} + {\left(- 2 + 3\right)}^{2} + {\left(7 - 1\right)}^{2}}$

$= \sqrt{{7}^{2} + {1}^{2} + {6}^{2}}$

$= \sqrt{49 + 1 + 36}$

$= \sqrt{86}$

$= 9.27 m$

The speed is

$v = \frac{d}{t} = \frac{9.27}{4} = 2.32 m {s}^{-} 1$