Calculating Displacement from a Velocity-Time Graph

The Physics Problem: Analyzing Runner's Displacement

Question:

Determine the total distance traveled by a runner in 24 seconds, given a velocity-time graph where the vertical scaling is set at 8 meters per second.

Solution: Using Area Under the Velocity-Time Graph

To solve this problem, we use the concept that the area under a velocity-time graph represents displacement:

Phase 1 - Understanding the Relationship

• The relationship between velocity and displacement is given by V = dx/dt, which means dx = Vdt. Therefore, the displacement (Δx) is the integral of Vdt, or the area under the velocity-time graph.

Phase 2 - Calculating the Area Under the Graph

• To find the runner's displacement, we calculate the total area under the given velocity-time graph for the 24-second interval.
• Depending on the shape of the graph (e.g., rectangles, triangles, trapezoids), we use appropriate geometric methods to calculate the area.

By applying these methods, we can determine the total distance traveled by the runner in the specified time.