1 of 1 gure What is the average velocity $$ v_{\mathrm{av}} $$ of the particle over the time interval $$ \Delta t=50.0 \mathrm{~s} $$ ? Express your answer in meters per second. View Available Hint(s) $$ v_{\mathbf{a v}}= $$ $$ \square $$ $$ \mathrm{m} / \mathrm{s} $$ Submit Part C

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To calculate the **average velocity** ($$ v_{\mathrm{av}} $$) of a particle over a time interval ($$ \Delta t $$), you need information about the particle's displacement ($$ \Delta x $$) during that time. The formula for average velocity is:

$$
v_{\mathrm{av}} = \frac{\Delta x}{\Delta t}
$$

Where:
- $$ \Delta x $$ is the displacement (in meters).
- $$ \Delta t $$ is the time interval (in seconds).

**Steps to Calculate Average Velocity:**

1. **Determine Displacement ($$ \Delta x $$):**
   - Displacement is the straight-line distance from the starting point to the ending point in a specific direction.
   - If you have the initial and final positions ($$ x_i $$ and $$ x_f $$), calculate displacement as:
     $$
     \Delta x = x_f - x_i
     $$

2. **Use the Average Velocity Formula:**
   - Once you have $$ \Delta x $$ and $$ \Delta t $$, plug them into the formula:
     $$
     v_{\mathrm{av}} = \frac{\Delta x}{\Delta t}
     $$

**Example:**

Suppose a particle moves from position $$ x_i = 100 $$ meters to $$ x_f = 300 $$ meters over a time interval of $$ \Delta t = 50.0 $$ seconds.

1. **Calculate Displacement:**
   $$
   \Delta x = x_f - x_i = 300\, \text{m} - 100\, \text{m} = 200\, \text{m}
   $$

2. **Calculate Average Velocity:**
   $$
   v_{\mathrm{av}} = \frac{200\, \text{m}}{50.0\, \text{s}} = 4\, \text{m/s}
   $$

**Final Answer:**
$$
v_{\mathrm{av}} = 4\, \text{m/s}
$$

*Please provide the displacement or additional information about the particle's motion if you need a more specific calculation.*
To find the average velocity $$ v_{\mathrm{av}} $$, use the formula: $$ v_{\mathrm{av}} = \frac{\Delta x}{\Delta t} $$ Where: - $$ \Delta x $$ is the displacement in meters. - $$ \Delta t $$ is the time interval in seconds. **Steps:** 1. Calculate displacement ($$ \Delta x $$) by subtracting the initial position from the final position. 2. Divide the displacement by the time interval to get the average velocity. **Example:** If a particle moves from 100 m to 300 m in 50.0 s: $$ \Delta x = 300\, \text{m} - 100\, \text{m} = 200\, \text{m} $$ $$ v_{\mathrm{av}} = \frac{200\, \text{m}}{50.0\, \text{s}} = 4\, \text{m/s} $$ **Final Answer:** $$ v_{\mathrm{av}} = 4\, \text{m/s} $$

1 of 1 gure What is the average velocity \( v_{\mathrm{av}} \) of the particle over the time interval \( \Delta t=50.0 \mathrm{~s} \) ? Express your answer in meters per second. View Available Hint(s) \[ v_{\mathbf{a v}}= \] \( \square \) \[ \mathrm{m} / \mathrm{s} \] Submit Part C

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