Introduction to Acceleration in Free Fall

In everyday scenarios and studies involving physics, the concept of acceleration is fundamental. Specifically, when a ball is dropped from a height, the acceleration it experiences is influenced by the principles of physics. Understanding how to calculate the average acceleration during a fall is a valuable skill. This article will guide you through the process of finding the average acceleration of a ball that falls from a height of 10 meters, achieving a velocity of 14 meters per second, and taking 1.42 seconds to hit the ground. By the end, you will not only understand the physics behind the fall but also learn to apply key formulas and principles.

Understanding Acceleration

Average acceleration is a measure of the change in velocity per unit time. It is defined as the change in velocity divided by the time taken, expressed mathematically as:

?v?t

where ?v is the change in velocity and ?t is the time taken.

Calculating Average Acceleration

To find the average acceleration of the ball during its fall, we need to use the given data:

Initial velocity, vos 0 m/s (since it is dropped) Final velocity, vos 14 m/s Time taken, ?t 1.42 seconds

The change in velocity (?v) is calculated as:

?v vos - voi 14 m/s - 0 m/s 14 m/s

The average acceleration (a) is then:

a ?v?t 14 m/s1.42 s ≈ 9.86 m/s2

Thus, the average acceleration of the ball during the fall is approximately 9.86 m/s2.

Alternative Approaches to Confirming the Result

The formula a v/t can also be used, yielding the same result:

Given v 14 m/s and t 1.42 s,

a 14 m/s1.42 s ≈ 9.86 m/s2

Another approach is to use the formula a 2h/t2, where h 10 m and t 1.42 s gives:

a 2ht2 2times;10 m(1.42 s)2 ≈ 9.92 m/s2

The third method uses a v2/2h with v 14 m/s and h 10 m to give:

a v22h (14 m/s)22times;10 m ≈ 9.8 m/s2

Average the three values: (9.86 9.92 9.8) / 3 ≈ 9.87 m/s2

Conclusion

From the calculations, we can conclude that the average acceleration of the ball during its fall is approximately 9.86 m/s2, closely approximating the standard value of gravitational acceleration on Earth, which is 9.8 m/s2. This aligns with the general understanding that the acceleration due to gravity is constant and can be calculated using the formula for average acceleration.