Calculate the average velocity at a particular time interval of a person if he moves from 10 m at 6 s to 24 m at 8 s along the x-axis?6 m/s9 m/s7 m/s50 m/s

1. ### Break Down the Problem

We need to calculate the average velocity of a person moving along the x-axis over a specific time interval. The data given includes:

• Initial position $x_i = 10 \, \text{m}$ at $t_i = 6 \, \text{s}$
• Final position $x_f = 24 \, \text{m}$ at $t_f = 8 \, \text{s}$

2. ### Relevant Concepts

The formula for average velocity $v_{avg}$ is given by: $v_{avg} = \frac{x_f - x_i}{t_f - t_i}$

3. ### Analysis and Detail

Now, substituting the given values into the average velocity formula: $v_{avg} = \frac{24 \, \text{m} - 10 \, \text{m}}{8 \, \text{s} - 6 \, \text{s}}$ $v_{avg} = \frac{14 \, \text{m}}{2 \, \text{s}}$ $v_{avg} = 7 \, \text{m/s}$

4. ### Verify and Summarize

Let’s verify the calculation:

• Displacement is $24 \, \text{m} - 10 \, \text{m} = 14 \, \text{m}$.
• Time interval is $8 \, \text{s} - 6 \, \text{s} = 2 \, \text{s}$.
• Using these values confirms $v_{avg} = 7 \, \text{m/s}$.

Final Answer

The average velocity is $\mathbf{7 \, \text{m/s}}$.