(d) average velocity of the trip 4. (a) Calculate the distance and average speed in \( m \cdot \mathrm{~s}^{-1} \) from A to B if the duration of the journey is 2 minutes (b) Aso calculate the displacement and average velocity from A to B . (Hint circumference of circle \( 2 \pi R \) or \( \pi \mathrm{O} \) )

To solve the problem of calculating the **distance**, **average speed**, **displacement**, and **average velocity** for a trip from point **A** to point **B**, we'll make use of the provided hint regarding the circumference of a circle. **Assumptions:** 1. The trip from **A** to **B** follows a semicircular path. 2. The radius of the circular path is denoted as \( R \). 3. The duration of the journey is **2 minutes**. If there are specific values for the radius \( R \) or other parameters, please provide them to refine the calculations. For now, we'll proceed with general formulas. ### 4. (a) Calculate the Distance and Average Speed **Distance Traveled (\( d \)):** Since the trip follows a semicircular path, the distance traveled is half the circumference of the circle. \[ \text{Circumference of a full circle} = 2\pi R \] \[ \text{Distance from } A \text{ to } B = \frac{1}{2} \times 2\pi R = \pi R \] **Average Speed (\( v_{\text{avg}} \)):** Average speed is the total distance traveled divided by the total time taken. \[ v_{\text{avg}} = \frac{d}{t} \] Given: - \( t = 2 \text{ minutes} = 120 \text{ seconds} \) \[ v_{\text{avg}} = \frac{\pi R}{120} \quad \text{(in meters per second)} \] ### 4. (b) Calculate the Displacement and Average Velocity **Displacement (\( \Delta x \)):** Displacement is the straight-line distance from the starting point **A** to the endpoint **B**. For a semicircular path, this is the diameter of the circle. \[ \Delta x = 2R \] **Average Velocity (\( \vec{v}_{\text{avg}} \)):** Average velocity is the displacement divided by the time taken. It's a vector quantity, meaning it has both magnitude and direction. \[ |\vec{v}_{\text{avg}}| = \frac{\Delta x}{t} = \frac{2R}{120} = \frac{R}{60} \quad \text{(in meters per second)} \] *Direction:* The direction of the average velocity vector is the straight line from **A** to **B**. ### Summary of Formulas - **Distance (\( d \))**: \( \pi R \) - **Average Speed (\( v_{\text{avg}} \))**: \( \frac{\pi R}{120} \, \text{m/s} \) - **Displacement (\( \Delta x \))**: \( 2R \) - **Average Velocity (\( \vec{v}_{\text{avg}} \))**: \( \frac{R}{60} \, \text{m/s} \) towards **B** from **A** ### Example Calculation If you provide a specific radius \( R \), we can plug in the numbers to get numerical values. For instance, let's assume \( R = 50 \) meters: - **Distance**: \( d = \pi \times 50 \approx 157.08 \) meters - **Average Speed**: \( v_{\text{avg}} = \frac{157.08}{120} \approx 1.31 \) m/s - **Displacement**: \( \Delta x = 2 \times 50 = 100 \) meters - **Average Velocity**: \( |\vec{v}_{\text{avg}}| = \frac{50}{60} \approx 0.83 \) m/s towards **B** from **A** Please provide additional details or specific values if you need a more precise calculation!