What is the velocity

Question

What is the velocity (in metres per second) of a Canadian Forces CF-18 fighter jet that travels 8.864 km [S] in 0.297 min?

Answer 1

This question needs some clarification. Velocity and speed are different things, and the data given in the question are not sufficient to compute velocity, only speed. So, I will assume they are asking for speed.

The average speed, s_av, of an object over some time interval is defined as the total distance traveled divided by the time that it took. For this question, we get

s_av = (8.864 km) / (0.297 min) = 29.845 km/min.

But they requested an answer in units of meters per second, so we need to convert to these units:

s_av = (8864 m) / (0.297 min × 60 s / min) = 497 m/s

(Here we only report three significant digits because the time had only three.)

Note that the distance can be accumulated along any path, not just a straight line. You can imagine a thin string that traces out the exact route taken, and the distance would be the length of this imaginary string, regardless of what contorted shape the path might have been. It is this distance that is used to compute the average speed.

This is in contrast with the average velocity, v_av , which is defined as the displacement divided by the time. Displacement, unlike distance or path length, is a vector that points from the starting position to the ending position. It doesn't matter what path was taken to get there, only the final position relative to the starting position. In fact, if an object travels around a closed path, like a racecar completing one lap of a track, then the displacement is zero, since the ending point is the same as the starting point!

Because displacement is a vector, so is the average velocity. Vectors have a direction as well as a length or magnitude. We don't have enough information in the problem to determine the direction of the fighter jet, so assume they are really asking for speed instead of velocity.

Answer 2

I present a detailed discussion of this problem in the short video on youtube.com at

https://www.youtube.com/watch?v=CPm7YaZZhAI

The basic ideas are the following, but they really need explaining, not just a couple of lines of text as is available in these short answers.

All unit conversion problems like this are easily solved and without confusion once you understand how they work, in particular all you will ever need are

1. The definition of the quantity you want to calculate, in this case the problem asks for velocity, but the author of the problem was slightly imprecise and you need to assume they are asking for average velocity specifically, and keep in mind that although the problem gives the distance as a displacement, the direction (south) is non-essential to the problem, apart from the fact that you would need to include it in your answer to make sure you got full credit. Also in this case it is helpful to remember that you are only working with three significant digits throughout, which saves a bit of writing.
2. The algebraic property that you can always multiply (for the real numbers we use in physics) a number by a factor equal to 1 without changing the value. That is all conversion factors are. Once you realize that, you can easily get whatever conversion factor you need.
3. An extra bonus is knowing that you can always check your work by using the plethora of online conversion tools. which I demonstrate in the video. However on a test, if you are being asked to show how to convert units, then you need to show you understand it. The rest of the time, for most work in science, you will be using a computer to do the conversions, much like you need to understand how to do long division and multiplication, but in practice a computer does it for you in work.

Answer 3

To find the velocity, first convert the distance to metres:

8.864 km × 1000 = 8864 m

Next, convert the time to seconds:

0.297 min × 60 = 17.82 s

Now calculate velocity:

v = d ÷ t = 8864 ÷ 17.82 ≈ 497.5 m/s

Since the jet travels south, the direction is [S].

Final Answer: The velocity of the CF‑18 fighter jet is approximately 498 m/s [S].

Answer 4

The key to questions like this is to set it up as fractions with the units, so that the units cancel out. So we have 8.864 km/ .297 min * 1 min/ 60 sec * 1000m/1 km so that the km cancel out and the min cancel out and we are left with 497.41 m/sec.