The acceleration of the hoop is calculated by determining the change in velocity over the given time period. Step-by-step Solution The change in velocity is found by subtracting the initial velocity from the final velocity: $\Delta v=v_{\text{final}}-v_{\text{initial}}=12\text{\ m/s}-2\text{\ m/s}=10\text{\ m/s}$. The acceleration is then calculated by dividing the change in velocity by the time taken: $a=\frac{\Delta v}{t}=\frac{10\text{\ m/s}}{6.0\text{\ s}}\approx 1.67\text{\ m/s}^{2}$.

Question

The acceleration of the hoop is calculated by determining the change in velocity over the given time period.                Step-by-step Solution      The change in velocity is found by subtracting the initial velocity from the final velocity: $\Delta v=v_{\text{final}}-v_{\text{initial}}=12\text{\ m/s}-2\text{\ m/s}=10\text{\ m/s}$. The acceleration is then calculated by dividing the change in velocity by the time taken: $a=\frac{\Delta v}{t}=\frac{10\text{\ m/s}}{6.0\text{\ s}}\approx 1.67\text{\ m/s}^{2}$.

GPT-4o mini · Answer

Your step-by-step solution for finding the acceleration of a hoop involves the correct application of the concepts of change in velocity and the formula for acceleration. Here’s a concise breakdown of the steps you mentioned:

Calculate the Change in Velocity ($\Delta v$): \[ \Delta v = v_{\text{final}} - v_{\text{initial}} = 12\ \text{m/s} - 2\ \text{m/s} = 10\ \text{m/s} \]
Calculate the Acceleration ($a$): The acceleration is calculated by dividing the change in velocity by the time taken. Given $t = 6.0\ \text{s}$: \[ a = \frac{\Delta v}{t} = \frac{10\ \text{m/s}}{6.0\ \text{s}} \approx 1.67\ \text{m/s}^2 \]

Therefore, the final result for the acceleration of the hoop is approximately $1.67\ \text{m/s}^2$.

This method is accurate and employs the correct formulas to reach the result. If you have any further questions or any additional concepts you'd like to explore, feel free to ask!