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

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The average velocity of the hour hand's tip from 12 p.m. to 6 p.m. is calculated as -0.8 j cm/hr, based on a displacement of 4.8 cm over six hours. The average acceleration, despite the constant speed, is derived from the change in velocity due to the hand's circular motion. The initial and final velocities are determined as Vi = 1.26i + 0j and Vf = -1.26i + 0j, respectively. The average acceleration is then calculated as -0.42 cm/hr² by dividing the change in velocity by the elapsed time. Understanding that acceleration occurs due to direction change is key to this calculation.
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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.
 
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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.
 
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I got it! Thank you!

The circumference is 4.8π so the velocity is 4.8π/12hrs=1.26cm/he
Vi= 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
 
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