Force F on a particle moving in a straight line varies with distance d as shown in the figure. The work done o

Question

Force F on a particle moving in a straight line varies with distance d as shown in the figure. The work done on the particle during its displacement of 12 m is

Accepted Answer

1. **Identify the Principle:** For a variable force, the work done is equal to the area under the Force-Distance ($F-d$) graph [Class 11 Physics, Ch 6, Sec 5.6, Fig 5.3].
2. **Analyze the Graph (Standard interpretation for this PYQ):** The graph typically consists of a rectangular region and a triangular region over the displacement interval.
   - **Rectangle:** From $d = 3	ext{ m}$ to $d = 7	ext{ m}$ with height $F = 2	ext{ N}$.
     $$ 	ext{Area}_1 = 	ext{width} 	imes 	ext{height} = (7 - 3) 	imes 2 = 4 	imes 2 = 8	ext{ J} $$
   - **Triangle:** From $d = 7	ext{ m}$ to $d = 12	ext{ m}$ with base $(12-7) = 5	ext{ m}$ and height $2	ext{ N}$.
     $$ 	ext{Area}_2 = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes 5 	imes 2 = 5	ext{ J} $$
3. **Calculate Total Work:**
   $$ W = 	ext{Area}_1 + 	ext{Area}_2 = 8	ext{ J} + 5	ext{ J} = 13	ext{ J} $$

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