To solve this problem, we need to analyze the given velocity-time graph and determine the corresponding acceleration-time graph.$\\$The velocity-time graph is a trapezoid, indicating three phases of motion:$\\$1. Acceleration phase: The velocity increases linearly from 0 to a maximum value.$\\$2. Constant velocity phase: The velocity remains constant at the maximum value.$\\$3. Deceleration phase: The velocity decreases linearly back to 0.$\\$Let's analyze each phase:$\\$• Acceleration Phase:$\\$The slope of the velocity-time graph is positive, indicating a constant positive acceleration.$\\$• Constant Velocity Phase:$\\$The slope is zero, indicating zero acceleration.$\\$• Deceleration Phase:$\\$The slope is negative, indicating a constant negative acceleration.$\\$Now, let's match these observations with the options:$\\$Option 1:$\\$• Positive constant acceleration, zero acceleration, then negative constant acceleration.$\\$Option 2:$\\$• Zero acceleration, then negative acceleration increasing in magnitude.$\\$Option 3:$\\$• Positive acceleration, zero acceleration, then positive acceleration again.$\\$Option 4:$\\$• Increasing acceleration, then constant acceleration.$\\$The correct acceleration-time graph should show:$\\$• A positive constant value, then zero, then a negative constant value.$\\$Therefore, the correct option is Option 1.