Maybe it's been a while since the last time you ran, so you have to slow down a little bit to two meters per second. When you get a little closer to home, you say: "No, Captain Antares wouldn't give up "and I'm not giving up either", and you start running at eight meters per second and you make it home just in time for the opening music.
These numbers are values of the instantaneous speed. The instantaneous speed is the speed of an object at a particular moment in time. And if you include the direction with that speed, you get the instantaneous velocity. In other words, eight meters per second to the right was the instantaneously velocity of this person at that particular moment in time.
Note that this is different from the average velocity. If your home was 1, meters away from school and it took you a total of seconds to get there, your average velocity would be five meters per second, which doesn't necessarily equal the instantaneous velocities at particular points on your trip. In other words, let's say you jogged 60 meters in a time of 15 seconds.
During this time you were speeding up and slowing down and changing your speed at every moment. Regardless of the speeding up or slowing down that took place during this path, your average velocity's still just gonna be four meters per second to the right; or, if you like, positive four meters per second.
Say you wanted to know the instantaneous velocity at a particular point in time during this trip. Add a comment. Active Oldest Votes. Improve this answer.
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Hot Network Questions. 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. This time interval at must be exceedingly small almost zero.
This is determined similarly to average velocity, but we narrow the period of time so that it approaches zero. If an object has a standard velocity over a period of time, its average and instantaneous velocities may be the same.
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