# Ambiguity in forumlas for average speed & average velocity

• e-zero
In summary: a) her average velocity while searching for the coin? b) her average speed while searching for the coin?
e-zero

On her way to school, a child discovered that her loonie is missing and there is a hole in her pocket. She turned back and walked 24 m east along the sidewalk. Then, she stopped for 18 s and decided to head back to school. After walking 11 m west, she found the loonie. If the child walked at a speed of 0.25 m/s, calculate,

a) her average velocity while searching for the coin?
b) her average speed while searching for the coin?

Obviously there are two parts where the student travelled.

First part:
x1=24m
v1=0.25m/s
t1=96s (after calculation)

Second part:
x2=11m
v2=0.25m/s
t2=44s (after calculation)

If I wanted to find the average velocity then I would use my velocity formula: (avg)v = (x2 - x1) / t2 - t1

but I have to be careful because writing (avg)v = (11m - 24m) / (96s - 44s) is wrong!

Is this a common mistake? Should I name my variables differently?

Why is the average velocity wrong? take the total displacement and divide by the total time

(24 - 11)/(96 + 18 + 44)

Do you think the answer is wrong because you didn't include the time she was stopped for?

As I read the problem, the 18 seconds standing still should also be averaged in, but that's irrelevant to the question that I think you are asking.

The formula that you are using intends that t1 and t2 are the start time and the end time of an interval. The "t1 - t2" clause will then give the total duration of that interval.

The t1 and t2 that you have calculated are the durations of two sub-intervals instead. The total duration of the interval would be given by "t1 + t2" in your case.

Yes, you need to keep track of the quantities that your variables denote and whether those are the same quantities that your formulas need as inputs or produce as outputs. If careful choice of variable names makes it easier to keep track, then by all means, choose your variable names carefully. Or actually write down what you are using them to mean. Careful documentation earns points and is a good habit to cultivate.

There are concepts of weighted averages in general and time-weighted averages in particular that might be of use if you are interested in understanding this more deeply.

So in this case I could just leave the variables as is?

Specifically, should I rename my variables for x1, x2 and t1, t2?? Because if you were to plug them 'directly' into the formula you would get the wrong answer.

It doesn't matter what you call them, as long as you understand the concept you will find the right answer. My advice is, never rely on an equation to be used blindly. In that equation, t1 and t2 are clock times, not time differences given in the question, so you need a new equation.

Ok, but I come from a programming background if if that was a sequence if code, then that formula would spit out the wrong answer. I'm just going to name the variables differently, in this case, to avoid confusion or loss of marks.

## 1. What is the difference between average speed and average velocity?

Average speed is a measure of how fast an object is moving over a given distance, while average velocity takes into account both the speed and direction of an object's motion. This means that an object could have the same average speed but different average velocities if it changes direction during its motion.

## 2. How is average speed calculated?

Average speed is calculated by dividing the total distance traveled by an object by the total time it took to travel that distance. This gives the overall average speed of the object throughout its entire journey.

## 3. How is average velocity calculated?

Average velocity is calculated by dividing the displacement (change in position) of an object by the total time it took to travel that distance. This takes into account the direction of the object's motion and gives the average velocity in a specific direction.

## 4. Why is there ambiguity in formulas for average speed and average velocity?

There is ambiguity in these formulas because they do not specify the exact path or trajectory of the object's motion. Average speed and average velocity only give an overall measure of the object's motion, but do not take into account any changes in direction or speed during the journey.

## 5. What are some real-world examples of ambiguity in average speed and average velocity?

A real-world example of ambiguity in average speed and average velocity would be a car traveling around a racetrack. The car's average speed may be the same on each lap, but its average velocity will differ as it changes direction. Another example could be a plane flying in a circular path, where its average speed remains the same but its average velocity changes as it moves in different directions.

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