What is the speed of an object that travels from #(4,-7,1) # to #(-1,3,-8) # over #6 s#?

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Answer 1 · 2016-02-05T22:16:15

#2.392m//s#

We may use the Euclidean metric in #RR^3# to find the distance between the two given points, assuming SI units, as

#x=d[(4,-1,7);(-1,3,8)]=sqrt((4-(-1))^2+(-7-3)^2+(1-(-8))^2)#

#=sqrt(25+100+81#

#=sqrt206# #m#.

We may now use the definition of speed (the rate of change in distance) to get

#v=x/t=sqrt206/6#

#=2.392m//s#