Displacement from velocity-time graph area

Steps:

• Identify displacement as the net area under the velocity-time curve from t=0 to t=20s, since initial displacement is zero.
• Divide the graph into shapes (e.g., triangles, rectangles) to compute areas; positive areas add, negative subtract.
• Calculate total area: for example, a positive triangle of base 10s and height 6m/s gives 30m², minus a negative trapezoid of 9m² yields net 21m.
• Confirm units: area in m/s × s = meters, matching displacement.

Why B is correct:

• Displacement equals the integral of velocity with respect to time (area under v-t curve), which integrates to 21m over 0-20s.

Why the others are wrong:

• A: Ignores net area, possibly only negative portion (-3m).
• C: Overestimates by including gross area without subtracting negative regions (24m).
• D: Assumes all positive area without any subtraction (27m).

Final answer: B