What is the speed of an object that travels from ( 4,-2,2) to ( -3, 8,-7 ) over 3 s?

1 Answer
Rudi d.
Apr 4, 2018

The answer would be the distance between the two points (or vectors) divided by the time. So you should get (sqrt(230))/3 units per second.

Explanation:

To get the distance between the two points (or vectors), just use the distance formula d = sqrt(x^2 +y^2 +z^2) on the difference between the two given points.

ie (x,y,z) = (-3-4, 8 -(-2),-7-2) = (-7,10,-9) ( note : it does not matter which way around we substract the points since the formula uses squares and thus eliminates any negative signs. We can do point A - point B or point B - point A)

Now applying the distance formula, we get
d = sqrt((-7)^2 +(10)^2 +(-9)^2) = sqrt(230)

Then all that is left is to divide by the time to get the answer.

Interesting fact: This distance formula is actually called the Euclidean Norm in the real normed space R^n, denoted by ||\bar(x)||_2.

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