Video Transcript
Which of the following speeds is the fastest? (A) One meter per second, (B) one kilometer per second, (C) one centimeter per second, (D) one millimeter per second.
Okay, so this question is giving us four speeds in four different units for speed. And we’re asked to work out which of them is the fastest.
We can recall that the speed of an object is the distance traveled by that object per unit of time. Mathematically, the speed is equal to the distance moved divided by the time taken to move that distance. This equation for speed means that the units of speed are always going to be some kind of distance units divided by some kind of time units. We can see that this is the case for all four of the speeds given to us in the question. In fact, all four of these speeds have the same time units. They are all measured as a distance traveled per second of time. So the greatest speed of these four possible options must be the one that has the greatest distance traveled per second.
If we look first at the speed given in option (A), we see that this speed is one meter per second. In other words, a distance of one meter is traveled per each second of time. Let’s compare this to the speed in option (B), which is one kilometer per second. One kilometer per second means that a distance of one kilometer is traveled per each second of time. We can recall that the prefix kilo- means 1000. And one kilometer is equal to 1000 meters. Replacing the one kilometer by 1000 meters, we see that a speed of one kilometer per second is equal to a speed of 1000 meters per second. 1000 meters traveled per second of time is clearly a greater distance per second than one meter traveled per second.
Now let’s have a look at the speed in option (C). This is one centimeter per second. We know that one meter is equal to 100 centimeters, which means that one centimeter is equal to one hundredth of a meter. One hundredth of a meter can also be written as 0.01 meters. So a speed of one centimeter per second, which means one centimeter of distance traveled per second of time, must be equal to 0.01 meters traveled per second. 0.01 meters is clearly a smaller distance to travel per second than either 1000 meters or one meter, making one centimeter per second or 0.01 meters per second the slowest speed so far.
Lastly, we have the speed in option (D), one millimeter per second. Since one meter is equal to 1000 millimeters, then one millimeter is equal to one thousandth of a meter, which we can also write as 0.001 meters. So the speed of one millimeter per second, which means one millimeter traveled per second of time, is the same as 0.001 meters traveled per second. This is a smaller distance traveled per second than in any of the other three options. And so one millimeter per second is the slowest of the four speeds.
So what we found then, ranking these speeds from slowest to fastest, is that the slowest speed is one millimeter per second. The next slowest is one centimeter per second. Then we have one meter per second. And finally, the fastest speed, which is our answer to this question, is one kilometer per second.
