To analyze the velocity-time graph of a vehicle and determine its acceleration and retardation, we need to understand how to interpret the graph. Since I cannot see the image, I will guide you through the general process of analyzing a velocity-time graph and how to calculate acceleration and retardation. ### Step-by-Step Explanation 1. **Understanding the Graph**: - A velocity-time graph plots velocity (y-axis) against time (x-axis). - The slope of the graph at any point gives the acceleration of the vehicle. A positive slope indicates acceleration, while a negative slope indicates retardation (deceleration). 2. **Identifying Sections of the Graph**: - Look for straight lines on the graph. Each straight line represents a constant acceleration or retardation. - Identify the segments where the vehicle is speeding up (acceleration) and where it is slowing down (retardation). 3. **Calculating Acceleration**: - To find the acceleration, use the formula: \[ a = \frac{\Delta v}{\Delta t} \] where \( \Delta v \) is the change in velocity and \( \Delta t \) is the change in time. - For example, if a segment of the graph shows a change from 0 m/s to 40 m/s over 5 seconds, the acceleration would be: \[ a = \frac{40 \, \text{m/s} - 0 \, \text{m/s}}{5 \, \text{s}} = \frac{40 \, \text{m/s}}{5 \, \text{s}} = 8 \, \text{m/s}^2 \] 4. **Calculating Retardation**: - Similarly, for retardation, identify a segment where the velocity decreases. Use the same formula: \[ r = \frac{\Delta v}{\Delta t} \] - For instance, if the velocity decreases from 40 m/s to 0 m/s over 5 seconds, the retardation would be: \[ r = \frac{0 \, \text{m/s} - 40 \, \text{m/s}}{5 \, \text{s}} = \frac{-40 \, \text{m/s}}{5 \, \text{s}} = -8 \, \text{m/s}^2 \] - The negative sign indicates a decrease in speed, which is why we refer to it as retardation. 5. **Analyzing the Options**: - Now, let's analyze the options given: - **A. 8.0 ms⁻², 4.0 ms⁻²**: This suggests a high acceleration and a lower retardation. - **B. 4.0 ms⁻², 8.0 ms⁻²**: This suggests a lower acceleration and a high retardation. - **C. 4.0 ms⁻², 2.0 ms⁻²**: This suggests moderate values for both acceleration and retardation. - **D. 2.0 ms⁻², 4.0 ms⁻²**: This suggests lower acceleration and moderate retardation. 6. **Choosing the Correct Answer**: - Based on the calculations from the graph, you would select the option that matches the calculated values for acceleration and retardation. If the graph shows an acceleration of 4.0 ms⁻² and a retardation of 2.0 ms⁻², then option C is correct. ### Why Other Options Are Incorrect: - **Option A**: If the graph does not show a steep enough slope for acceleration to be 8.0 ms⁻², this option is incorrect. - **Option B**: If the vehicle does not decelerate at a rate of 8.0 ms⁻², this option is also incorrect. - **Option D**: If the acceleration is higher than 2.0 ms⁻², this option is incorrect. ### Common Pitfalls: - Misreading the graph: Ensure you accurately interpret the slopes. - Confusing acceleration with retardation: Remember that acceleration is positive when speeding up and negative (retardation) when slowing down. - Not using consistent units: Always ensure that time is in seconds and velocity in meters per second. ### Revision Summary: - The slope of a velocity-time graph indicates acceleration (positive slope) or retardation (negative slope). - Use the formula \( a = \frac{\Delta v}{\Delta t} \) to calculate both acceleration and retardation. - Carefully analyze the graph to determine the correct values for acceleration and retardation. - Ensure to check all options against your calculations to select the correct answer.