WEBVTT
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Which of the following is a symbol for a unit of speed?
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(A) Meters per second, (B) meters per second squared, (C) second meters, (D) meter seconds, (E) seconds per meter.
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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.
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In order to work out what unit speed could have, we should start by recalling the definition of speed.
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Speed is defined as the total distance moved by an object divided by the total time taken to travel that distance.
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Now this quantity here in the numerator, the total distance moved by the object, is going to have units of distance.
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Meanwhile, this quantity in the denominator, the total time taken to travel that distance, will have units of time.
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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.
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For example, let’s consider the simple equation 𝐴 equals 𝐵.
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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.
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In our case, we’ve said that speed is equal to a distance divided by a time.
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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.
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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.
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We’ll start with option (A), which is units of meters per second.
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Now, meters are a unit of distance, and seconds are a unit of time.
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So if we have meters per second, then that is indeed a unit of distance divided by a unit of time.
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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.
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In order to be thorough, we should go through and check the remaining options just to be sure.
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If we look at option (B), we see that this is units of meters per second squared.
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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.
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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.
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If we now look at option (C), we find that we have units of seconds multiplied by units of meters.
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So this is units of time multiplied by units of distance.
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And again looking at this equation for the units, we see that these are not units of speed.
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Looking now at option (D), we see that we have units of meters multiplied by units of seconds.
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When we multiply together two quantities, the order of multiplication doesn’t matter.
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And the same is true when we’re talking about units.
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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).
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And we have already established that these are not units of speed.
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Finally, let’s look at option (E).
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This is unit of seconds per meter.
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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.
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And if we look at our equation for the units, we see that this is not a unit of speed.
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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.
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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.