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Distance vs. Displacement

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Charles Scruggs

on 7 September 2014

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Transcript of Distance vs. Displacement

Laws of Motion
Distance (A Scalar Quantity)
Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Example: If an object is moved in the pattern show in this figure, you could say that the object has moved 10 meters total distance.


Displacement
(A Vector Quantity)


Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.

Example: Using the previous drawing of the object that moved in the rectangular path:

So once the object has completed it motion around the rectangle, how many meters has it been DISPLACED from its original position?
Practice Problems
Distance and Displacement
Even though I moved a distance of 7 units total

(4 units to the right, then climbed a hill 3 units tall)

My displacement is only 5 units from my original position at the base of the first hill!

Check:

a^2 + b^2 = c^2

4 squared = 16 3 squared = 9 9 + 16 = 25 The square root of 25 = 5

5 meters is the total displacement.
Assume the figure moves 4 meters right.
We all use language daily to tell others about direction.

Whether up, down, left, right, forward, backward, or sideways--there are numerous ways to describe the motion and direction of an object.

Given this fact, physicists also need to use specific terminology to precisely describe the motion of objects.

The first step to understanding motion is distinguishing distance from displacement. Let's take a moment to clarify this beginning concept.
OBJECT
Now assume the figure climbs 3 meters up.
What's the difference?
OBJECT
If you said zero meters you'd be right. Though its traveled 10 meters, it ended its path exactly where it began. That's displacement; the distance of an object from its original position after moving.
A machinist, travels from home to work at the factory and back again every work day. What is the total distance the motor cyclist travels daily?
What is the total displacement of the motor cyclist's daily commute?
A cross country runner leaves school for a 10-mile run. They end their run at the Sonic one mile from school. What is the total distance they ran? What is their displacement?
400 m, The road taken to work is 200 m both ways--totaling 400m there and back.
0 m. The motorcyclist's point of origin is the exact same as the destination.
Total Distance Ran = 10 miles
Displacement = 1 mile (the distance from the point of origin to the destination)
Success!
Conclusions (Distance and Displacement)
Next Lesson:

Laws of Motion
Average Speed
vs. Average Velocity
See you tomorrow!
Displacement = 5 meters
Distance?
Displacement?
A mountain climbing expedition establishes a base camp and two intermediate camps, A and B. Camp A is 4,000 m west of and 3,000 m above base camp. Camp B is 2,000 m east of and 1,000 m higher than Camp A. Determine the displacement between base camp and Camp B.
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