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What is the speed of an object that travels from #( -9,4,-6) # to #( -9,-9,2) # over #3 s#?

Answer 1

William Audy

#5.09ms^(-1)#

#"Speed"="Distance"/"Time"#

#"Time"=3s#

#"Distance"=sqrt((Deltax)^2+(Deltay)^2+(Deltaz)^2)#

#Deltax=-9-(-9)=-9+9=0# #Deltay=-9-4=-13# #Deltaz=2-(-6)=2+6=8#

#"Distance"=sqrt(0^2+(-13)^2+8^2)=sqrt(169+64)=sqrt(233)#

#"Speed"=sqrt(233)/3~~5.09ms^(-1)#

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Answer 2

Charlotte Aaron

To calculate the speed of an object traveling from one point to another, you first need to find the displacement vector between the two points. Then, divide the magnitude of the displacement vector by the time taken to travel that distance. The displacement vector is the final position minus the initial position. Given the initial position (-9, 4, -6) and the final position (-9, -9, 2), the displacement vector is (0, -13, 8). The magnitude of this vector is √(0^2 + (-13)^2 + 8^2) = √(0 + 169 + 64) = √233. Dividing this magnitude by the time taken, which is 3 seconds, gives the speed of the object: √233 / 3 ≈ 7.22 meters per second.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.