This picture is helpful:. The positions of the words in the triangle show where they need to go in the equations. To find the speed, distance is over time in the triangle, so speed is distance divided by time. To find distance, speed is beside time, so distance is speed multiplied by time. Users' questions. Esther Fleming January 4, Table of Contents. Previous Article Is composting a sustainable practice? Next Article What is the largest tribe in Afghanistan? Back To Top.
The first column gives a physical description of a time span, the second is the measurement of that time span in convenient units, and the third represents the time span expressed in seconds using scientific notation. Play Activity. The previous activity gave you a chance to think about some different timescales you might encounter in your daily life or as part of this class.
It asked you to compare them and rank them. This is a useful skill to have when you are trying to understand how one process or event might relate to another. However, in the previous activity, you were given all of the times in a common unit, seconds. Normally, things are not so convenient. You will generally have to convert to a common unit before you can make a comparison. The next set of activities gives you additional practice with this useful skill.
In the next set of activities, you will work with the relationship between distance, speed, and time. These quantities can be described in various ways. While the units we use to describe a speed are arbitrary, we generally use whatever is most convenient. The next several activities are intended to give you a better understanding of speed and its relation to distance and time.
If you have been driving on the highway for 1 hour and have traveled 30 miles, what is your average speed? Now the goal is to determine how much time it would take you to get to various places in the Universe, if you were traveling on foot if it were possible! Drag and drop the travel time tiles for the following places you might like to visit.
Their distances are:. There are several worked examples below to get you started. How much time would it take to get to the nearest star 4 light-years away traveling at light-speed? How much time would it take to get to the nearest star 4 light-years away traveling at half light-speed?
The Stargazers Club is discussing a galaxy that is far, far away. Keisha has pulled up an image of it on her phone and tells the group that it is 10 billion light-years away. The distances to stars and galaxies are so large that even light, traveling almost , km every second, still requires years to travel to them.
That means when we look at a star, Alpha Centauri for example, we are not seeing it as it is. We are seeing it as it was 4 years ago. The same is true for the Sun, of course. We do not see it as it is, we see it as it was 8 minutes ago. That has certain implications for our observations of the Universe; if the Sun were to shut off at this moment, we would not know it for 8 minutes.
That is because any photons that just left the Sun would not arrive for 8 minutes, and until they got here we would have no way to know that the Sun had gone out. This concept is so important in astronomy that it is given a special name: lookback time. We would say that the lookback time to the Sun is 8 minutes.
To Alpha Centauri, the lookback time is about 4 years. But what about other parts of the Milky Way Galaxy, or other galaxies?
Well, the typical lookback time to objects inside our Galaxy is several tens of thousands of years. That is because our Galaxy is about , light-years across. As a result, light requires up to about , years to reach one part of the Galaxy from another part. For external galaxies, the lookback times are even bigger. As the seconds tick away the velocity does not change. So it's just moving five meters per second. Now, my question to you is how far does this thing travel after five seconds?
So after five seconds-- so this is one second, two second, three seconds, four seconds, five seconds, right over here. So how far did this thing travel after five seconds? Well, we could think about it two ways. One, we know that velocity is equal to displacement over change in time. And displacement is just change in position over change in time. Or another way to think about it-- If you multiply both sides by change in time-- you get velocity times change in time, is equal to displacement.
So what was of the displacement over here? Well, I know what the velocity is-- it's five meters per second. That's the velocity, let me color-code this.
That is the velocity. And we know what the change in time is, it is five seconds. And so you get the seconds cancel out the seconds, you get five times five-- 25 meters-- is equal to 25 meters.
And that's pretty straightforward. But the slightly more interesting thing is that's exactly the area under this rectangle right over here. What I'm going to show you in this video, that is in general, if you plot velocity, the magnitude of velocity.
So you could say speed to versus time. Or let me just stay with the magnitude of the velocity versus time. The area under that curve is going to be the distance traveled, because, or the displacement. Because displacement is just the velocity times the change in time. So if you just take out a rectangle right over there. So let me draw a slightly different one where the velocity is changing. So let me draw a situation where you have a constant acceleration.
The acceleration over here is going to be one meter per second, per second. So one meter per second, squared. And let me draw the same type of graph, although this is going to look a little different now. So this is my velocity axis.
I'll give myself a little bit more space. I'm just going to draw the magnitude of the velocity, and this right over here is my time axis. So this is time. And let me mark some stuff off here. So one, two, three, four, five, six, seven, eight, nine, ten.
0コメント