# Finding average speed

1. Feb 15, 2015

### 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!

2. Feb 15, 2015

### DaveC426913

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.

3. Feb 15, 2015

### Nathanael

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.

4. Feb 15, 2015

### haruspex

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.