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

1 Answer
Jan 21, 2016

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#.