# What is the speed of an object that travels from (4,-7,1)  to (-1,3,-8)  over 6 s?

Feb 5, 2016

$2.392 m / s$

#### Explanation:

We may use the Euclidean metric in ${\mathbb{R}}^{3}$ to find the distance between the two given points, assuming SI units, as

x=d[(4,-1,7);(-1,3,8)]=sqrt((4-(-1))^2+(-7-3)^2+(1-(-8))^2)

=sqrt(25+100+81

$= \sqrt{206}$ $m$.

We may now use the definition of speed (the rate of change in distance) to get

$v = \frac{x}{t} = \frac{\sqrt{206}}{6}$

$= 2.392 m / s$