physics question?

Question

A physicist measures the instantaneous velocity of an object in three different places along its journey. The velocities were 2 m/sec, 4 m/sec, and 8 m/sec. She then measures the object's average velocity throughout the journey. Which of the following values is most likely to be that average velocity: 1m/sec, 3 m/sec, or 16m/sec?

Answer 1

3m/s

Answer 2

First of all let me say that I love the idea of actually measuring instantaneous velocity. You really must ask the person who posed the problem how this is done.

I am sure that lots of people will happily say that it cannot be less than 2 or more than 8 therefore it must be 3, however, there is no evidence to indicate where along the journey the "instantaneous" measurements were made. To be absolutely correct, it has to be said that all of the average velocities proposed are possible, and without further information all are equally likely.

It may be that the intention of the question was to show you how you can be misled by incomplete information, in which case my answer is correct. If this was not the intention of the question, then the questioner really needs to learn how to pose questions that can be answered.

Answer 3

Think about "average" being "less extreme", and more towards the middle ground.

Now we have 3 data points, 2, 4, and 8. Somehow the average velocity of the entire journey is more likely to be around the "middle" of all points of measurements. 1 and 16 are both outside the range of the measured data, so we'd need to believe that either extremely slow velocities exist, so that the average be dragged down to 1, or extremely high velocities outside the 3 data points exist, so the average got dragged all the way up to 16.

For the number 3, which is within the range of the observed data, it could be the average if we believe the 3 data points are "representative", meaning they are typical velocities along the journey.

So, depending what you believe, you'd decide on which is the "likely average". In this case, it is logical to believe the 3 data points are representative, and that no extreme velocities are observed outside the range of the 3 observed velocities. Thus, 3 m/sec is likely the average speed.

Hope this helps.

Answer 4

Doing a straight average will yield you an average velocity of 4.7 m/s (2 + 4 + 8 = 14, div by 3 = 4.66). So the closest answer would be 3.

Which makes sense if the object is not travelling at a constant velocity. That's why you take an average.

But 4.7 (my answer) is not exactly 3 (choice), which leads me to this point...
If there's any other info in the question, it may yield a different and more complete answer (time b/t measurements, is it accelerating, how long is the total journey compared to the measured intervals, etc...).

Answer 5

Well, it is a very poorly thought out question.

First of all, velocity involve direction also which is not mentioned in the question.

So, we may assume the given values are that of instantaneous speeds, and we are to calculate the average speed. This is again ill defined and incomplete; We need more data, in fact the instantaneous speed at every instant, or the acceleration in between. So, it is simply not possible to calculate the average velocity or average speed in the given situation.

By definition, average speed = Totals distance covered/Total time taken.
Mathematically, Vav = S/t
or Vav = (S1 + S2 + S3 + .. )/(t1 + t2 + t3 +...)

Under some situations, it may be possible for the average speed to have any one of the three given values.

Answer 6

Lets be reasonable here. The average will be somewhere in between the highest and lowest values measured. With that in mind we can eliminate the 1 m/s and 16 m/s because they don't fit in the range of measurements. That leaves the 3 m/s as the answer.

Answer 7

the average velocity can't be more than 8m/sc( the highest) and less than 2m/sec( the lowest)