Thank you ahead of time for taking to look at this. For this following problem we were given an answer however I am almost positive the given answer is wrong. It doesn't even make sense. So here is the question:

The sweep-second hand of a clock is 3.4 cm long. What are the magnitudes of:

a) the magnitude of the average velocity vector [not the average speed!] of the hand tip over a 12 second interval?

Firstly isn't the magnitude of average velocity = the average speed? I don't see how those could be different but the question seems to indicate this

The answer given is $.333 cm/s$. This seems highly improbable given that the circumference is $21.36 cm$ so in $12s$ the second hand tip would have only traversed $3.96 cm$ around the circumference in 12 seconds considering a second hand completes a complete revolution every minute I don't see how this could be right.

Instead I would say the magnitude of the velocity vector = $\frac{(2\pi r)}{t}$

Where r is radius and t is time to complete revolution so:

$v = \frac{2\pi 3.4}{1} = 21.36 cm/s $

Which seems a lot more realistic

Part b) further confuses me as they state:

the average acceleration of the hand tip over a 12 second interval?

and they give an answer of $0.0349 cm/s^2$

It is my understand that $a = \frac{v^2}{r}$ so even using their own value for velocity

$a = \frac{0.333^2}{3.4} = 0.0326$ which is a different answer.

Am I missing something?

Thanks!

## Best Answer

Yes, you are missing something and I get the given answer. But this is a "homework" problem, so hints only.

The wording of the question is important. For instance the magnitude of the average velocity vector over 60 seconds would be exactly zero. Or to put it another way, if I travel at constant speed to a point, and then turn round and come back at the same speed, then the average speed is finite but the average velocity is zero.

i.e. you need to work out an expression for the velocity vector at an arbitrary angle and then find the average velocity vector over a 12 second (72 degree angle) period and

only thenfind the magnitude of that.