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

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.*