Which of the following is a symbol for a unit of speed? (A) Meters per second, (B) meters per second squared, (C) second meters, (D) meter seconds, (E) seconds per meter.
The question presents us with a load of different symbols for units and asks us which of the available options is a symbol for a unit of speed. In order to work out what unit speed could have, we should start by recalling the definition of speed. Speed is defined as the total distance moved by an object divided by the total time taken to travel that distance. Now this quantity here in the numerator, the total distance moved by the object, is going to have units of distance. Meanwhile, this quantity in the denominator, the total time taken to travel that distance, will have units of time. Whenever we have any equation, we know that the units on the left-hand side must be the same as the units on the right-hand side.
For example, let’s consider the simple equation 𝐴 equals 𝐵. We can only know if quantity 𝐴 is indeed equal to quantity 𝐵 if we can measure these two quantities in the same way as each other, in other words, if the units of 𝐴 are equal to the units of 𝐵. In our case, we’ve said that speed is equal to a distance divided by a time. Since we know that in this equation the units on the left-hand side must agree with the units on the right-hand side, then we have that the units of speed must be equal to units of distance divided by units of time. Now we just need to go through the different options given to us in the question and see which of these is equal to a unit of distance divided by a unit of time.
We’ll start with option (A), which is units of meters per second. Now, meters are a unit of distance, and seconds are a unit of time. So if we have meters per second, then that is indeed a unit of distance divided by a unit of time. Since we’ve already said that when we have a unit of distance divided by a unit of time, we get a unit of speed, then we know that meters per second is a valid unit for speed. In order to be thorough, we should go through and check the remaining options just to be sure.
If we look at option (B), we see that this is units of meters per second squared. And since meters are units of distance and seconds are units of time, then what we have here is units of distance divided by units of time squared. Comparing with this equation here for the units of speed, we see that this does not give a unit of speed, so meters per second squared cannot be our answer.
If we now look at option (C), we find that we have units of seconds multiplied by units of meters. So this is units of time multiplied by units of distance. And again looking at this equation for the units, we see that these are not units of speed. Looking now at option (D), we see that we have units of meters multiplied by units of seconds. When we multiply together two quantities, the order of multiplication doesn’t matter. And the same is true when we’re talking about units. So the units here in option (D) meters multiplied by seconds are just the same as the units of seconds multiplied by meters that we had in option (C). And we have already established that these are not units of speed.
Finally, let’s look at option (E). This is unit of seconds per meter. Since we know that seconds are a unit of time and meters are a unit of distance, then seconds per meter is a unit of time divided by a unit of distance. And if we look at our equation for the units, we see that this is not a unit of speed. So the only one of the potential answers presented to us that we have found to have units of speed is given to us in option (A) meters per second. And so our answer to the question “which of the following is a symbol for a unit of speed?” is given here by option (A) meters per second.