# What is the Average Speed of an Object Traveling 12 Meters in 9 Seconds?

• erandall
In summary, a middle school science teacher without a science or math background is designing a lesson to teach students how to answer a question involving speed and distance. The teacher has noticed the ambiguity in the chart and is concerned about teaching an explanation that may be incorrect. After analyzing the answer choices, the teacher believes the correct answer to be 1.33 m/s, but is unsure why this formula works. The teacher is seeking a simple and concrete explanation that would make sense to a student with limited math and science education. The teacher also points out that the starting time and distance are arbitrary and do not affect the average speed calculation.
erandall
1. I'm a middle school science teacher without a science or math background. My goal here is to avoid teaching an explanation that kids will have to unlearn later in their academic career. I'm designing a lesson to teach students how to answer this question:

2. Limitation: students are NOT expected to understand velocity, they only need to manipulate the Speed= distance/time equation.

3. As far as I can tell from the answer choices, the answer should be 1.33 m/s, which is the ending speed. Logically, this makes sense to me: if the object was able to travel 12 meters in 9 seconds, then that final data point is essentially averaging the time that it takes to travel the total distance, despite any changes in rate that may occur throughout the line.

However, I seem to remember--and googling seems to confirm-- that this isn't actually the way mathematically to find the average slope of a function. So why does this work? Or am I actually incorrect about the answer?

If possible, could you please explain in terms that would make sense to a student who hasn't had a math or science education beyond the 6th grade. The more simple and concrete, the better!

The chart is ambiguous.
The only recorded data points are from 3s onwards. And at that point, it was already 4m distant from some reference point. You cannot say that is has moved 12m.

You can say that is has moved (12-4=) 8m in (9-3=) 6s, which is, in fact 1.33m/s, but not for the reason you state.

The object doesn't travel 12 meters in 9 seconds (this just coincidentally gives the right answer).

As it travels from A to C it only travels 12-4=8 meters (because it starts out at 4 meters already). And it doesn't take 9 seconds because it's at point A at t=3 seconds, so it only takes 9-3=6 seconds. Thus the average speed is 8/6 m/s.

The important thing to realize is that the correct form of "average speed = distance / time" should actually be "average speed = (change in distance) / (change in time)"
(Well, this isn't strictly true. For example, if you're running in a circle, the average speed is clearly not zero, but the change in distance will sometimes be zero so this formula will be wrong. But I'm sure if you don't expect them to understand velocity, then you will keep everything 1 dimensional, in other words, movement is restricted to straight lines.)

The starting time (3 seconds) and the starting distance (4 meters) are completely arbitrary. We could have said the starting time was 15 years, and the starting distance was 100 miles, but this has no effect on the average speed.

DaveC426913 said:
The chart is ambiguous.
The only recorded data points are from 3s onwards. And at that point, it was already 4m distant from some reference point. You cannot say that is has moved 12m.

You can say that is has moved (12-4=) 8m in (9-3=) 6s, which is, in fact 1.33m/s, but not for the reason you state.
Quite, and this makes it a poorly constructed question for multiple choice. The student has a high chance of picking the right answer for the wrong reason.

## 1. What is the formula for finding average speed?

The formula for finding average speed is total distance traveled divided by total time taken. It can be represented as v = d/t, where v is the average speed, d is the total distance traveled, and t is the total time taken.

## 2. How do you find the total distance traveled?

The total distance traveled can be found by adding all the distances traveled during the given time period. For example, if a car travels 50 km in the first hour and 70 km in the second hour, the total distance traveled would be 50 km + 70 km = 120 km.

## 3. What units are used to measure average speed?

Average speed is typically measured in units of distance per unit time, such as kilometers per hour (km/h) or meters per second (m/s).

## 4. Can average speed be negative?

No, average speed cannot be negative as it represents the average rate of motion, which is always a positive value. However, if an object changes direction during its motion, its average velocity (which takes into account direction) can be negative.

## 5. How does finding average speed differ from finding average velocity?

Finding average speed involves calculating the total distance traveled divided by the total time taken, while finding average velocity involves calculating the total displacement (change in position) divided by the total time taken. Average velocity takes into account direction, while average speed does not.

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