Her trip took 8 hours. What was her average speed? That was easy! Lisa Carr averaged a speed of 55 miles per hour.
Yet, she averaged a speed of 55 miles per hour. The above formula represents a shortcut method of determining the average speed of an object. Since a moving object often changes its speed during its motion, it is common to distinguish between the average speed and the instantaneous speed. The distinction is as follows. You might think of the instantaneous speed as the speed that the speedometer reads at any given instant in time and the average speed as the average of all the speedometer readings during the course of the trip.
Moving objects don't always travel with erratic and changing speeds. Occasionally, an object will move at a steady rate with a constant speed. That is, the object will cover the same distance every regular interval of time.
If her speed is constant, then the distance traveled every second is the same. The runner would cover a distance of 6 meters every second. If we could measure her position distance from an arbitrary starting point each second, then we would note that the position would be changing by 6 meters each second. This would be in stark contrast to an object that is changing its speed. An object with a changing speed would be moving a different distance each second. The data tables below depict objects with constant and changing speed.
Now let's consider the motion of that physics teacher again. Velocity is defined as a vector measurement of the rate and direction of motion. Put simply, velocity is the speed at which something moves in one direction. The speed of a car traveling north on a major freeway and the speed a rocket launching into space can both be measured using velocity. As you might have guessed, the scalar absolute value magnitude of the velocity vector is the speed of motion. In calculus terms, velocity is the first derivative of position with respect to time.
You can calculate velocity by using a simple formula that includes rate, distance, and time. The most common way to calculate the constant velocity of an object moving in a straight line is with this formula:.
Speed, velocity, and acceleration are all related to each other, though they represent different measurements. Be careful not to confuse these values with each other. Velocity measures motion starting in one place and heading toward another place. The practical applications of velocity are endless, but one of the most common reasons to measure velocity is to determine how quickly you or anything in motion will arrive at a destination from a given location.
Velocity makes it possible to create timetables for travel, a common type of physics problem assigned to students. Average speed, however, is very different from average velocity.
Average speed is the distance traveled divided by elapsed time. We have noted that distance traveled can be greater than displacement. So average speed can be greater than average velocity, which is displacement divided by time. Your average velocity, however, was zero, because your displacement for the round trip is zero. Displacement is change in position and, thus, is zero for a round trip. Thus average speed is not simply the magnitude of average velocity.
Figure 3. During a minute round trip to the store, the total distance traveled is 6 km. The displacement for the round trip is zero, since there was no net change in position.
Thus the average velocity is zero. Another way of visualizing the motion of an object is to use a graph. A plot of position or of velocity as a function of time can be very useful. For example, for this trip to the store, the position, velocity, and speed-vs.
Note that these graphs depict a very simplified model of the trip. We are also assuming that the route between the store and the house is a perfectly straight line. Figure 4. Position vs. Note that the velocity for the return trip is negative.
If you have spent much time driving, you probably have a good sense of speeds between about 10 and 70 miles per hour. But what are these in meters per second? To get a better sense of what these values really mean, do some observations and calculations on your own:. A commuter train travels from Baltimore to Washington, DC, and back in 1 hour and 45 minutes. The distance between the two stations is approximately 40 miles. Note that the train travels 40 miles one way and 40 miles back, for a total distance of 80 miles.
Give an example but not one from the text of a device used to measure time and identify what change in that device indicates a change in time. There is a distinction between average speed and the magnitude of average velocity. Thus, the number calculated above is not the speed of the car, it's the average speed for the entire journey.
In order to emphasize this point, the equation is sometimes modified as follows…. Read it as "vee bar is delta ess over delta tee". This is the quantity we calculated for our hypothetical trip.
In contrast, a car's speedometer shows its instantaneous speed , that is, the speed determined over a very small interval of time — an instant. Ideally this interval should be as close to zero as possible, but in reality we are limited by the sensitivity of our measuring devices. Mentally, however, it is possible to imagine calculating average speed over ever smaller time intervals until we have effectively calculated instantaneous speed.
This idea is written symbolically as…. If you haven't dealt with calculus, don't sweat this definition too much. There are other, simpler ways to find the instantaneous speed of a moving object. On a distance-time graph, speed corresponds to slope and thus the instantaneous speed of an object with non-constant speed can be found from the slope of a line tangent to its curve. We'll deal with that later in this book.
In order to calculate the speed of an object we need to know how far it's gone and how long it took to get there. A wise person would then ask….
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