What is the speed of an object that travels from #( -9,0,1) # to #( -1,4,3 ) # over #2 s#?

1 Answer
Apr 19, 2016

Answer:

speed: #sqrt(21) "units"/"sec" ~~4.58 "units"/"sec"#

Explanation:

Distance between #(-9,0,1)# and #(-1,4,3)#
is
#color(white)("XXX")d=sqrt((-1-(-9))^2+(4-0)^2+(3-1)^2)#
#color(white)("XXXx")=sqrt(8^2+4^2+2^2)#
#color(white)("XXXx")=sqrt(64+16+4)#
#color(white)("XXXx")=sqrt(84)#
#color(white)("XXXx")=2sqrt(21)# (units)

Assuming a constant speed, #s#
#color(white)("XXX")"speed" = "distance"/"time"#
So
#color(white)("XXX")s=(2sqrt(21) " units")/(2 " sec")#

#color(white)("XXX")=sqrt(21) "units"/"sec"#

#color(white)("XXX")sqrt(21)~~4.58# (using a calculator)