# What is the speed of an object that travels from ( 1, -2, 3 )  to ( -5, 6, 7 )  over 4 s?

Jan 25, 2016

$2.693 m / s$

#### Explanation:

The distance between the 2 given 3-dimensional points may be found from the normal Euclidean metric in ${\mathbb{R}}^{3}$ as follows :

x=d( (1,-2,3);(-5,6,7) )=sqrt((1-(-5))^2+(-2-6)^2+(3-7)^2)

=sqrt(36+64+16

$= \sqrt{116} m$ , (Assuming the SI units are used)

Therefore the speed of the object by definition would be the rate of change in distance and given by

$v = \frac{x}{t} = \frac{\sqrt{116}}{4} = 2.693 m / s$.