How Is Average Acceleration Calculated for a Clock's Hour Hand Movement?

[ianperez]

Homework Statement

What are the average velocity and average acceleration of the tip of the 2.4-cm-long hour hand of a clock in the interval from 12p.m. to 6p.m.

I'm given the displacement which is 4.8 cm.
I know the motion takes six hours
I set my x-axis at three-o-clock and my y-axis at 12

Homework Equations

Average velocity = displacement / change in time
Average acceleration = change in velocity / change in time

I

The Attempt at a Solution

The answer I get for velocity agrees with the back of the book:

Avg Velocity = -0.8 j cm/hr

But I have no clue how they get an average acceleration of -0.42 i cm/hr².
I don't understand why there would be an average acceleration if the hand moves at a constant speed. I understand that a change in direction changes acceleration, but I'm missing something.

 

[NascentOxygen]

Hi ianperez. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

Acceleration = (change in velocity of a point on the tip) / elapsed time

So you first need to determine magnitude and direction of the tip's velocity at the two times given.

If the tip experienced no acceleration, it would not follow a curved path.

 

[ianperez]

I got it! Thank you!

The circumference is 4.8π so the velocity is 4.8π/12hrs=1.26cm/he
V_{i= 1.26i + 0j
Vf = -1.26i + 0j
Acceleration = (change in velocity of a point on the tip) / elapsed time
A= -1.26-1.26 / 6hrs = -0.42cm/hr}

 

[NascentOxygen]

looks good ☺[/size][/color]