Test Pilot Neil Armstrong (later to become a famous astronaut) is seen here next to the X-15 ship after a research flight. The servo-actuated ball nose, seen at Armstrong's right hand, provided accurate measurement of air speed at hypersonic speeds. The X-15 was flown over a period of nearly 10 years, and set the world's unofficial speed record of 4,250 mph.

### Average Velocity

In ordinary language, the words *speed* and *velocity* both refer to how fast an object is moving, and are often used interchangeably. In physics, however, they are fundamentally different. **Speed** is the magnitude of an object's motion, with no regard for the direction. **Velocity**, on the other hand, includes direction. It is a vector, and thus must have a magnitude and a direction.

Average speed is calculated by dividing the total distance travelled by the time interval. For example, someone who takes 40 minutes to drive 20 miles north and then 20 miles south (to end up at the same place), has an average speed of 40 miles divided by 40 minutes, or 1 mile per minute (60 mph). Average velocity, however, involves total displacement, instead of distance. It is calculated by dividing the total displacement by the time interval. In this example, the driver's displacement is zero, which makes the average velocity zero mph.

Neither average speed nor average velocity implies a constant rate of motion. That is to say, an object might travel at 10 m/s for 10 s and then travel at 20 m/s for 5 s and then travel at 100 m/s for 5 s. This motion would cover a distance of 700 m in 20 s and the average speed would be 35 m/s. We would report the average speed during this 20 s interval to be 35 m/s and yet at no time during the interval was the speed necessarily 35 m/s.

Constant velocity is very different from average velocity. If an object traveled at 35 m/s for 20 s, it would travel the same distance in the same time as the previous example but in the second case, the object's velocity would always be 35 m/s.

**Example: ** The position of a runner as a function of time is plotted as moving along the \begin{align*}x\end{align*}-axis of a coordinate system. During a 3.00 s time interval, the runner’s position changes from \begin{align*}x_1 = 50.0 \ \text{m}\end{align*} to \begin{align*}x_2 = 30.5 \ \text{m}\end{align*}. What was the runner’s average velocity?

**Solution:**

\begin{align*}\text{Displacement} = 30.5 \ \text{m} - 50.0 \ \text{m} = -19.5 \ \text{m}\end{align*} (the object was traveling back toward zero)

\begin{align*}\Delta t = 3.00 \ \text{s}\end{align*}

\begin{align*}v_{\text{ave}}=\frac{\Delta x}{\Delta t}=\frac{-19.5 \ \text{m}}{3.00 \ \text{s}}=-6.50 \ \text{m/s}\end{align*}

#### Summary

- Average speed is distance divided by time.
- Average velocity is displacement divided by time.

#### Practice

The url below is a physics classroom discussion of speed versus velocity with a short animation.

http://www.physicsclassroom.com/Class/1DKin/U1L1d.cfm

Use this resource to answer the questions that follow.

http://www.youtube.com/watch?v=BWP1tN7PZps

- The velocity versus time graph in the video is divided into six sections. In how many of these sections is the velocity constant?
- In how many sections of the graph is the velocity zero?
- What does the area under the curve of a velocity versus time graph represent?

#### Review

- On a one day vacation, Jane traveled 340 miles in 8.0 hours. What was her average speed?
- An object on a number line moved from
*x*= 12 m to*x*= 124 m and moved back to*x*= 98 m. The time interval for all the motion was 10 s. What was the average velocity of the object? - An object on a number line moved from x = 15 cm to x = 165 cm and then moved back to x = 25 cm, all in a time of 100 seconds.
- What was the average velocity of the object?
- What was the average speed of the object?