What is its speed at point

Just as we need to distinguish between instantaneous velocity and average velocity, we also need to distinguish between instantaneous speed and average speed. Instantaneous speed is the magnitude of instantaneous velocity. At that same time his instantaneous speed was 3. 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. Give an example that illustrates the difference between these two quantities. Does its speedometer measure speed or velocity? If you divide the total distance traveled on a car trip as determined by the odometer by the time for the trip, are you calculating the average speed or the magnitude of the average velocity?

Under what circumstances are these two quantities the same? How are instantaneous velocity and instantaneous speed related to one another? How do they differ? If we take a road trip of km and need to be at our destination at a certain time, then we would be interested in our average speed.

However, we can calculate the instantaneous speed from the magnitude of the instantaneous velocity:. Some typical speeds are shown in the following table.

When calculating instantaneous velocity, we need to specify the explicit form of the position function x t. The following example illustrates the use of Figure. Strategy Figure gives the instantaneous velocity of the particle as the derivative of the position function. Looking at the form of the position function given, we see that it is a polynomial in t.

Therefore, we can use Figure , the power rule from calculus, to find the solution. We use Figure to calculate the average velocity of the particle. The instantaneous velocity is the derivative of the position function and the speed is the magnitude of the instantaneous velocity. We use Figure and Figure to solve for instantaneous velocity. The velocity of the particle gives us direction information, indicating the particle is moving to the left west or right east.

The speed gives the magnitude of the velocity. By graphing the position, velocity, and speed as functions of time, we can understand these concepts visually Figure. The reversal of direction can also be seen in b at 0. But in c , however, its speed is positive and remains positive throughout the travel time. We can also interpret velocity as the slope of the position-versus-time graph.

The slope of x t is decreasing toward zero, becoming zero at 0. This analysis of comparing the graphs of position, velocity, and speed helps catch errors in calculations. The graphs must be consistent with each other and help interpret the calculations. The slope of the position graph is the velocity. A rough comparison of the slopes of the tangent lines in a at 0. Speed is always a positive number. There is a distinction between average speed and the magnitude of average velocity.

Give an example that illustrates the difference between these two quantities. Average speed is the total distance traveled divided by the elapsed time. If you go for a walk, leaving and returning to your home, your average speed is a positive number.

If you divide the total distance traveled on a car trip as determined by the odometer by the elapsed time of the trip, are you calculating average speed or magnitude of average velocity? Under what circumstances are these two quantities the same? How are instantaneous velocity and instantaneous speed related to one another? How do they differ? A woodchuck runs 20 m to the right in 5 s, then turns and runs 10 m to the left in 3 s. 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…. What do you mean by how far? Do you want the distance or the displacement? Speed and velocity are related in much the same way that distance and displacement are related. Speed is a scalar and velocity is a vector. Speed gets the symbol v italic and velocity gets the symbol v boldface.

Average values get a bar over the symbol. Displacement is measured along the shortest path between two points and its magnitude is always less than or equal to the distance. The magnitude of displacement approaches distance as distance approaches zero. That is, distance and displacement are effectively the same have the same magnitude when the interval examined is "small". Since speed is based on distance and velocity is based on displacement, these two quantities are effectively the same have the same magnitude when the time interval is "small" or, in the language of calculus, the magnitude of an object's average velocity approaches its average speed as the time interval approaches zero.

Speed and velocity are both measured using the same units. The SI unit of distance and displacement is the meter. The SI unit of time is the second. The SI unit of speed and velocity is the ratio of two — the meter per second.

This unit is only rarely used outside scientific and academic circles. Sometimes, the speed of an object is described relative to the speed of something else; preferably some physical phenomenon.