# What is the speed of an object that travels from ( 4,-2,2)  to ( -3, 8,-7 )  over 3 s?

Apr 4, 2018

The answer would be the distance between the two points (or vectors) divided by the time. So you should get $\frac{\sqrt{230}}{3}$ units per second.

#### Explanation:

To get the distance between the two points (or vectors), just use the distance formula $d = \sqrt{{x}^{2} + {y}^{2} + {z}^{2}}$ on the difference between the two given points.

ie $\left(x , y , z\right) = \left(- 3 - 4 , 8 - \left(- 2\right) , - 7 - 2\right) = \left(- 7 , 10 , - 9\right)$ ( note : it does not matter which way around we substract the points since the formula uses squares and thus eliminates any negative signs. We can do point A - point B or point B - point A)

Now applying the distance formula, we get
$d = \sqrt{{\left(- 7\right)}^{2} + {\left(10\right)}^{2} + {\left(- 9\right)}^{2}} = \sqrt{230}$

Then all that is left is to divide by the time to get the answer.

Interesting fact: This distance formula is actually called the Euclidean Norm in the real normed space ${R}^{n}$, denoted by $| | \setminus \overline{x} | {|}_{2}$.