# Plural or single—at velocities or at velocity [duplicate]

Hypothetical Case

There are 2 types of cars that move at constant velocity on the road. The first type move at velocity 90 (km/hr), and the second type move at velocity 95 (km/hr).

How it is proper in the formal writing:

The cars move at velocities 90 (km/hr), and 95 (km/hr).

or

The cars move at velocity 90 (km/hr), and 95 (km/hr).

I don't know because they are 2 velocities–plural, but the second option seems more English style.

Edit

replace 'same' by 'constant' as

• The speed of a car depends on the driver - do you mean their maximum speeds? Commented Jun 28, 2021 at 14:41
• Unless this is physics, we say: move at speeds of x and y, Commented Jun 28, 2021 at 15:05
• If these were two velocities, then it would be better to say velocities than velocity in this context. However, these are speeds not velocities. The word velocity means something slightly different. Commented Jun 29, 2021 at 5:34
• You mean speed, not velocity. Commented Jun 29, 2021 at 9:47

That's a needless problem. When you say X km/h, that's a velocity. Just say

The cars move at 90 km/hr and 95 km/hr.

However, if you want to include the word velocity, a more idiomatic expression would be
The cars move at velocities of 90 and 95 km/hr.

Note that the units don't need to be repeated when the values are right next to each other.

• 1) Have to write velocity (vector) to emphisize velocity, because otherwise a student may choose speed (scalar) 2) Why 2 option is wrong? (The cars move at velocity 90 (km/hr), and 95 (km/hr))
– Ben
Commented Jun 28, 2021 at 23:05
• If you use option 2, you should use plural "velocities". Omitting "of" is possible, but it's easier to read and understand with "of". Putting units in parentheses isn't correct, and repeating the units when they don't change between figures isn't necessary and decreases readability. As to point 1), yes, there's a difference between the scalar and vector quantities, but unless the element of direction is important in the statement, it might as well be omitted. Since a road is more or less one dimensional, if the cars are going the same direction, you might as well use "speed" or nothing. Commented Jun 28, 2021 at 23:44
• On the other hand, on a linear road, if the cars are going in opposite directions, the "velocities" should be stated as 95 km/hr and -90 km/hr, or vice versa. Commented Jun 28, 2021 at 23:45
• @Ben, if you are going to be pedantic, I have to say that 90 km/hr is not a velocity -- velocity is a vector. 90 km/hr is simply a speed. Commented Jun 29, 2021 at 0:20
• If the velocities (rather than the speeds) are so important, why not tell the students the velocities? For example, "The cars move at velocities of 90 km/hr due east and 95 km/hr due north." Commented Jun 29, 2021 at 11:48

What is clearest is to write

The first and second cars move at speeds of 90 and 95 km/hr respectively

It corresponds exactly to the mathematical notation

||v_1||= 90 km/hr and ||v_2|| = 95 km/hr

The so-called velocities that you are talking about are irrelevant because what is being discussed are speeds. There are no directional components involved.