A particle moves along $ X $-axis from $ x=0 $ to $ x=5 \mathrm{~m} $ under the influence of force given by $ F=\left(7-2 x+3 x^{2}\right) \mathrm{N} $. The work done in the process is

Question

A particle moves along $ X $-axis from $ x=0 $ to $ x=5 \mathrm{~m} $ under the influence of force given by $ F=\left(7-2 x+3 x^{2}\right) \mathrm{N} $. The work done in the process is, $ 70 \mathrm{~J} $, $ 270 \mathrm{~J} $, $ 35 \mathrm{~J} $, $ 135 \mathrm{~J} $

MARKS App · Accepted Answer

The given force varies with distance Therefore, work done, W = ∫ 0 x = 5 F . d x = ∫ 0 5 7 - 2 x + 3 x 2 d x = 7 x - 2 x 2 2 + 3 x 3 3 0 5 = 7 × 5 - 5 2 + 5 3 - 0 = 135 J

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