On a velocity versus time graph the quantity the area between the graph line and the x-axis represents the change in _______ of the object .
position (or location)
On a velocity versus time graph, the area between the graph line and the x-axis represents the change in displacement of the object.
To understand why, it's helpful to remember that velocity represents the rate of change of displacement over time. Mathematically, velocity can be calculated by finding the derivative of the displacement function with respect to time. Consequently, the area under the velocity graph represents the integral of velocity, which is equivalent to finding the change in displacement.
To calculate the change in displacement using the graph, you can estimate the area between the graph line and the x-axis. First, identify the region between the graph line and the x-axis for the time interval you are interested in. Then, divide this region into smaller, easier-to-calculate shapes like rectangles and triangles. For each shape, calculate its area (base times height for rectangles, one-half base times height for triangles) and sum up these areas to determine the total change in displacement.
Keep in mind that if the velocity is positive, the area will lie above the x-axis, representing positive displacement. Conversely, if the velocity is negative, the area will be below the x-axis, indicating negative displacement.