91Ó°ÊÓ

Average velocity in physics is a concept often used to describe the motion of an object over a particular interval of time. It is defined as the total displacement divided by the time taken to cover that displacement. In mathematical terms, it is expressed as:

• \( v_{avg} = \frac{s}{t} \)

where \( s \) stands for distance traveled and \( t \) is the time taken.
For objects moving with uniform acceleration, average velocity can also be calculated using the initial and final velocity, \( v_i \) and \( v_f \) respectively, using the formula:

• \( v_{avg} = \frac{v_i + v_f}{2} \)

This gives a good estimate of how fast something is moving on average, even if the speed changes during the motion. In our given problem, it is given that the average velocity is \( 0.34 \, \text{m/s} \), providing us a glimpse into the overall effectiveness of the motion over a total journey of \( 3.06 \, \text{m} \).

Kinematic equations are used to calculate various aspects of motion in physics, especially when an object is moving with constant acceleration. These equations are essential for breaking down the different components of motion, helping us predict the future position, velocity, or acceleration of moving objects.
In our problem, several kinematic equations come into play:

• Average velocity: \( v_{avg} = \frac{s}{t} \)
• Change in velocity: \( v_f - v_i \)
• Calculation of acceleration: \( a = \frac{v_f - v_i}{t} \)

Understanding how to manipulate these formulas is key.
In the problem, the known quantities such as distance, average velocity, and change in velocity helped us deduce the time taken, which we then used to find the uniform acceleration.

Motion with constant acceleration refers to a scenario where an object's velocity changes at a consistent rate over time. This makes predicting the object's future position and velocity straightforward because the change is uniform. Uniform acceleration thus simplifies many calculations in physics and forms an integral part of kinematic studies.
The core principle is that since the velocity changes at a constant rate, the equations of motion can be used consistently:

• Distance-time relationship: \( s = v_{avg} \cdot t \)
• Acceleration calculation: \( a = \frac{v_f - v_i}{t} \)

In the exercise provided, we use the concept of uniform acceleration to determine how the velocity changes affect the overall motion. By breaking down the problem, understanding the uniform change in velocity, and using the known distance and average velocity, we achieve a complete picture of this constant acceleration motion. Ultimately, the solving of the problem involves calculating the acceleration correctly by understanding these principles, yielding \( 0.02 \, \text{m/s}^2 \).