Final answer:
To find the slopes and deflections using the moment area method, calculate the area under the velocity vs. time graph; geometric shapes represent displacements and slopes indicate acceleration.
Step-by-step explanation:
To determine the slopes and deflections using the moment area method, we follow these steps:
- Draw a sketch of the velocity vs. time graph for the given problem.
- Identify the known quantities such as initial velocity, time intervals, and shape of the velocity graph.
- Resolve the area under the curve into simple geometric shapes over the given time intervals.
- Calculate the area of each shape to determine the displacement. For instance, use the formula area of rectangle = length × width and area of triangle = 0.5 × base × height.
- Sum the areas of these shapes to obtain the net displacement over the entire time interval.
- Use the tangent line at a specified time to calculate the instantaneous acceleration, since the slope of the velocity graph at any point is equal to the instantaneous acceleration at that point.
To determine negative acceleration, measure the flat area below the slope and use the appropriate kinematic equation based on the motion characteristics.