# Explaining usefullness of displacement and velocity

1. Sep 14, 2014

### supernova88

I know the difference between distance and displacement, and speed and velocity, but I'm struggling how to explain the usefulness of displacement and velocity in the real world? For instance, our cars count the distances they travel, not displacement as one might see on a map, while airplanes plot their paths according to the distances they cover flying over the Earth's surface, not the displacement from one city to the next as if you drew a straight line through the crust. Similarly, if I told someone how fast I travel from one city to the next (whether driving or flying or whatever) based on velocity rather than speed, my answer may seem ridiculously slow or wildly fast depending on how much displacement I cover in some time versus the actual distance of my route. What's an easy way to explain, then, the reason we bother having displacement and velocity in the first place and some good examples where they make sense?

2. Sep 14, 2014

### Staff: Mentor

Cars cannot measure the displacement directly, but it would be really useful if they could - you could know your position on the map without needing GPS.
In an airplane (or a ship), knowing the speed is nice, but you are also interested in the direction - you have to find the velocity, and you have to keep track of displacement to know where you are (again, GPS made that easier).

The same is true for nearly everything else that is not bound to roads, rails, canals or similar. You have to know the direction of its current motion/total displacement.

Subtracting two speeds often gives a wrong answer if you are interested in relative motion - you have to take the velocities. And so on.

3. Sep 14, 2014

### A.T.

What do you mean by "in the real world"? Physics is done in the real world. Displacement and velocity are used extensively in physics. Displacement is used to calculate work and energy used. Velocity is used to calculate momentum and predict outcome of collisions.

If you mean a device that captures displacement / velocity, like odometers / speedometers capture distance / speed, then I guess an inertial navigation system is the closest example:

4. Sep 14, 2014

### supernova88

To be more specific, A.T., I'm trying to explain displacement/velocity to people who've never heard of them before. Because these kids don't yet know anything about energy and work, I'm trying to keep things simple, but I'm struggling to find everyday examples to point to. I could, for instance, say that the distance and displacement a track athlete runs are different depending on where he/she stars and finishes, or the velocity of one's trip from home into the city is different than the actual speeds they experience on the road. I guess I'm just trying to anticipate the part where the kids ask why anyone would care or need to know displacement or velocity. After all, we don't measure gas usage in displacement, or we don't drive negative 65 mph when we turn around and go home. Are there any cases, aside from when distance/displacement or speed/velocity happen to be the same thing (i.e. driving in a straight line), where it's important to know displacement and velocity?

5. Sep 14, 2014

### A.T.

Cue sports?
http://en.wikipedia.org/wiki/Cue_sports

6. Sep 14, 2014

### supernova88

Hmmmm, good one