# What is the speed of an object that travels from ( -9,4,-6)  to ( -5,1,-2 )  over 3 s?

May 25, 2016

The speed is 2.13 m/s.

#### Explanation:

The distance between two points in the space is given by
$d = \sqrt{{\left({x}_{1} - {x}_{2}\right)}^{2} + {\left({y}_{1} - {y}_{2}\right)}^{2} + {\left({z}_{1} - {z}_{2}\right)}^{2}}$.
This is the Pitagora's theorem in three dimensions.
The speed is simply the space (in this case the distance) divided by the time.

$d = \sqrt{{\left(- 9 + 5\right)}^{2} + {\left(4 - 1\right)}^{2} + {\left(- 6 + 2\right)}^{2}} = \sqrt{{\left(- 4\right)}^{2} + {3}^{2} + {\left(- 4\right)}^{2}} = \sqrt{41} \setminus \approx 6.4 m$
$v = \frac{6.4}{3} \setminus \approx 2.13$ m/s