Video transcript Let's work through another few scenarios involving displacement, velocity, and time, or distance, rate, and time. So over here we have, Ben is running at a constant velocity of three 3 meters per second to the east. And just as a review, this is a vector quantity. They're giving us the magnitude and the direction. If they just said 3 meters per second, then that would just be speed. So this is the magnitude, is 3 meters per second. And it is to the east. So they are giving us the direction.
So this is a vector quantity. And that's why it's velocity instead of speed. How long will it take him to travel meters. So let's just remind ourselves a few things. And I'll do it both with the vector version of it. And maybe they should say, how long will it take them to travel meters to the east, to make sure, to make it clear, that it is a vector quantity.
So that it's displacement, as opposed to just distance, but we'll do it both ways. So one way to think about it, if we think about just the scalar version of it, we said already that rate or speed is equal to the distance that you travel over some time. I might write t there. But it's really a change in time. So sometimes some people would write a little triangle, a delta there, which means change in time.
But that's implicitly meant when you just write over time like that. So rate or speed is equal to distance divided by time.
Now, if you know-- they're giving us in this problem, they're giving us the rate. If we think about the scalar part of it, they're telling us that that is 3 meters per second.
And they're also telling us the time. Or, sorry, they're not telling us the time. They are telling us the distance, and they want us to figure out the time. So they tell us the distance is meters. And so we just have to figure out the time. We're dealing with the rate or speed and distance. So we have 3 meters per second is equal to meters over some change in time.
And so we can algebraically manipulate this. We can multiply both sides times time. Multiply time right over there. And then we could, if we all-- well, let's just take it one step at a time. So 3 meters per second times time is equal to meters because the times on the right will cancel out right over there. And that makes sense, at least units-wise, because time is going to be in seconds, seconds cancel out the seconds in the denominator, so you'll just get meters.
So that just makes sense there. So if you want to solve for time, you can divide both sides by 3 meters per second. And then the left side, they cancel out. On the right hand side, this is going to be equal to divided by 3 times meters. That's meters in the numerator. And you had meters per second in the denominator. If you bring it out to the numerator, you take the inverse of this. So that's meters-- let me do the meters that was on top, let me do that in green.
Mathematically, finding instantaneous velocity, v , at a precise instant t can involve taking a limit, a calculus operation beyond the scope of this text.
However, under many circumstances, we can find precise values for instantaneous velocity without calculus. In physics, however, they do not have the same meaning and they are distinct concepts. One major difference is that speed has no direction. Thus speed is a scalar. 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. Write your answer Related questions.
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