Explain why displacement is a vector quantity?

1 Answer
Jacob F. · Media Owl
May 22, 2014

Displacement is defined as the final distance vector minus the initial distance vector.

Let's say you're driving to work in the morning. You first drive north for #5# miles, and then drive east for another #5# miles.

Now let's say that when you get there, you take out a street map. If you were to draw a straight line starting at your house and ending at your workplace, that line would be your displacement vector. That straight line would be #sqrt(50)# miles long, (use the Pythagorean theorem) and it would be pointing northeast. Since the line has a direction, it needs to be a vector quantity. If it weren't a vector quantity, you wouldn't be able to draw it on a map at all, because it would just be a number.

Another reason why displacement needs to be a vector is because it's defined as a subtraction of two vectors, and a vector minus another vector is always a vector.

Very good explanation with good figures can be on this site http://www.physicsclassroom.com/class/1DKin/Lesson-1/Distance-and-Displacement

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