Question

A force \(F_x\) acts on a particle such that its position \(x\) changes as shown in the figure. The work done by the particle as it moves from \(x = 0\) to \(20 \, m\) is

• A. 37.5 J
• B. 10 J
• C. 15 J
• D. 22.5 J
• E. 45 J

Hint:

Work from graph = total area under curve (consider sign carefully).

Answer 1

Answer: (E)

Concept: Work done is equal to the area under the force vs displacement graph: \[ W = \int F \, dx \]

Step 1: Understand graph regions. From graph:
• \(0 \to 5\): force increases linearly to 3 N (triangle)
• \(5 \to 15\): constant force = 3 N (rectangle)
• \(15 \to 20\): force decreases to zero (triangle)

Step 2: Area of first triangle. \[ W_1 = \frac{1}{2} \times 5 \times 3 = 7.5 \, J \]

Step 3: Area of rectangle. \[ W_2 = 10 \times 3 = 30 \, J \]

Step 4: Area of second triangle. \[ W_3 = \frac{1}{2} \times 5 \times 3 = 7.5 \, J \]

Step 5: Total work. \[ W = 7.5 + 30 + 7.5 = 45 \, J \] Since last triangle may represent decreasing force but still positive, total work: \[ \boxed{45 \, J} \]