Video Transcript
Which of these is a unit of speed? (A) Seconds per kilometer, (B) kilometers per meter, (C) kilometers per second, (D) kilometer seconds.
Okay, so this question is giving us four different units and asking us to identify which of them is a unit of speed. We can recall that the speed of an object is defined as the distance traveled by that object per unit of time. Mathematically, speed is equal to the distance moved divided by the time taken to move that distance. We can use this equation to help us figure out which of these units can be a unit of speed.
Since speed is equal to distance divided by time, then any unit of speed must be equal to a distance unit divided by a time unit. A distance unit is anything that can be used to measure a length or distance. This includes units such as meters, centimeters, kilometers, and miles, among others. Similarly, a time unit is any unit that can be used to measure time. For example, this could be seconds, hours, or years. The point is that any of these or any other distance unit divided by any of these or any other time unit will give us a valid unit of speed.
So with that in mind, let’s look at the four options given to us and see which of them fits this condition. Option (A) is units of seconds per kilometer. That’s a unit of time divided by a unit of distance. Since it isn’t a unit of distance divided by a unit of time, then seconds per kilometer cannot be a unit of speed.
Option (B) is units of kilometers per meter, so that’s a unit of distance divided by another unit of distance. Again, that’s not a unit of distance divided by a unit of time, so kilometers per meter cannot be a unit of speed.
The units in option (C) are kilometers per second. The kilometer is a unit of distance, and that’s divided by the second, a unit of time. So kilometers per second is a unit of distance divided by a unit of time, which means that it is a unit of speed.
Lastly, let’s look at the unit in option (D). This is a kilometer second, which is units of kilometers multiplied by units of seconds. The kilometer is a distance unit, and the second is a time unit. So the kilometer second is a distance unit multiplied by a time unit, which is not a unit of speed.
In summary then, we found that only one of the four possible units given to us was a unit of speed. This unit is the kilometer per second, which is the answer given in option (C).
