**Interpreting the graph** I need to analyze the problem's graph, which depicts velocity versus time with triangular shapes. Starting from an initial position of 1 m, the task is to find the final position at t=10 s. Displacement can be calculated as the area beneath the velocity-time graph. I’m trying to reconstruct the times and velocities from the blurry graph. It looks like the velocity ranges from -0.5 to +0.5 m/s, with a peak at t=3 s at 0.5 m/s.**Analyzing the velocity graph** The graph indicates that from t=4 to t=6, the velocity is zero. Then, there's a triangular negative section from t=6 to 9, reaching a minimum of around -0.5 m/s at t=8, and returning to zero by t=10. I think the negative triangle might span from t=6 to t=9, with a small positive rise from t=9 to t=10. The earlier triangular positive section is from t=2 to t=4, peaking at 0.5 m/s, creating a symmetrical pattern.**Calculating displacement areas** I’m evaluating the displacement areas from the graph: - For 0-2 seconds, the velocity is 0, giving an area of 0. - From 2-4 seconds, I have a triangular area calculated as (1/2) * base * height: the base is 2 s, and the height is about 0.5 m/s, resulting in an area of 0.5 m. - From 4-6 seconds, the area is still 0. - From 6-10 seconds, the negative triangle has a base of 4 s and a height of 0.5 m, giving an area of -1.0 m. So overall, the total displacement is -0.5 m from the initial position.**Summarizing displacement calculation** I've calculated the area of the negative triangle from 6 to 10 seconds to be -1.0 m, leading to a final position of 0.5. Since I'm asked for a numeric answer without units, I'll just state "0.5." Now, I want to craft an explanation with step-by-step details on how to compute displacement by summing the triangular areas. I’ll mention reading from the image and clarify the segments: v=0 from 0-2, triangular from 2-4 with a peak at 0.5, zero from 4-6, and negative triangular from 6-10 reaching -0.5.**Final answer preparation** I’m ready to produce the final answer: 0.5. Here’s how I’ll display the calculations: - Displacement equals the net area under the v-t curve. - The area of the positive triangle is 0.5 m. - The area of the negative triangle is -1.0 m. - This gives a net displacement of -0.5 m. - Therefore, the final position \( x_f = x_0 + Δx = 1 + (-0.5) = 0.5 \). So, the final numeric answer is 0.5, and I might mention that it’s in meters, although I won’t type the units.