Final answer:
The acceleration of the Atwood's machine is approximately 2.84 m/s^2.
Step-by-step explanation:
The acceleration of an Atwood's machine can be calculated using the formula:
acceleration = (m2 - m1) * g / (m1 + m2)
Where m1 and m2 are the masses of the two objects, and g is the acceleration due to gravity.
Substituting the given values, we have:
acceleration = (10.9 kg - 4.43 kg) * 9.8 m/s^2 / (4.43 kg + 10.9 kg)
Simplifying this expression gives us an acceleration of approximately 2.84 m/s^2.