Question

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

Answer 1

First of all let us find find the distance between the two given points.
The distance formula for Cartesian coordinates is

`d=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2`
Where `x_1, y_1,z_1`, and `x_2, y_2,z_2` are the Cartesian coordinates of two points respectively.
Let `(x_1,y_1,z_1)` represent `(8,4,1)` and `(x_2,y_2,z_2)` represent `(6,-1,6)`.
`implies d=sqrt((6-8)^2+(-1-4)^2+(6-1)^2`
`implies d=sqrt((-2)^2+(-5)^2+(5)^2`
`implies d=sqrt(4+25+25`
`implies d=sqrt(54` units

Hence the distance is `sqrt54` units.

`Speed=(Distance)/(Time)`

`Speed=sqrt54/4=1.837(units)/sec`

If the units is meter then
`Speed=1.837m/s`.