  In studying motion, we learned about speed and velocity. In this lesson we are going to investigate these a bit more. But before we get started, we need to learn a few scientific terms and symbols.

In math we have many different symbols that make it easier to state a problem. For example, we could say: "Subtract five from fourteen and then divide the answer by three and then add seven."

Or, we could just use the symbols: Science has similar symbols. Of course there are all of the common math symbols, but there are other symbols that make it easier to write equations. Sometimes these symbols are straight forward. For example, we use the letter "v" for "velocity" and "t" for "time". But some symbols are unique to that word or phrase. When we want to determine the speed of an object, we need to take the change in distance (how far it went), and divide it by the change in time (how long it took to get there). We use the △ symbol to say "change in". So d means "change in distance" and △t means "change in time". REVIEW QUESTION

1. How would you "say" (in a sentence) the following formula. (Example: "4 + 2 = 6" would be read: "Four plus two equals six.")

Speed measures how fast an object moves. To measure speed you must have: 1. Reference points.
2. The change in distance (or distance traveled).
3. The change in time (or time it took to get from one reference point to the other).

In the figure below the two reference points are A and B. Notice that the total change in distance from point A to B is 40 miles. This is not "as the crow flies", but is the actual distance that the car travels. The car left at 2:30 pm and arrived at 3:30 pm. So the total change in time is one hour. To figure the average speed of the car we divide forty miles by one hour to get forty miles per hour, or 40 mph. It is important to note that in the above calculations we found the "average" speed. It is quite likely that the instantaneous speed or speed of the car at any given moment might have been higher at one point (say 50 mph) and lower (say 30 mph) at another.

REVIEW QUESTION 2. What are the three things needed in order to find the average speed of a car? Velocity is the speed of an object from one point to another in a straight line. For example, let's say you walk from the driver's door of a car around to the passenger door on the other side. If the distance was 15 feet and it took you 5 seconds, then your speed would be 15 feet/5 seconds or 3 feet per second. However, since velocity is the change in position (not the total distance), your position would have changed only 5 feet (from one door to the other) but it still took 5 seconds. Therefore, your velocity would have been 5 feet/5 seconds or 1 foot per second.

The formula for velocity looks like this.  You may have figured this out already, but this straight line distance between two points we call displacement. Displacement is the straight line change in position of an object. Notice in the example below that the distance between point A and B is much greater than the displacement (straight line change). The figure to the left is the same figure you saw earlier in this lesson. Notice that the total miles traveled was forty. However, the total change in displacement was only 28.3 miles. This is because displacement is measured in straight line quantities.

So even though we figure the average speed of the car at forty miles per hour, its average velocity was only 28.3 miles per hour . One more important thing regarding velocity is that it is also a measure of direction. If point B is directly southeast of point A, then we would say "the velocity of the car was 28.3 miles per hour in a southeast direction.

REVIEW QUESTION 3. What is the difference between distance and displacement?