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Question: A position dependent force \(F = 7 - 2 x + 3 x ^ { 2 }\) newton acts on a small body of mass 2 kg an...

A position dependent force F=7−2x+3x2F = 7 - 2 x + 3 x ^ { 2 } newton acts on a small body of mass 2 kg and displaces it from x=0x = 0 to . The work done in joules is

A

70

B

270

C

35

D

135

Answer

135

Explanation

Solution

W=∫05Fdx=∫05(7−2x+3x2)dxW = \int _ { 0 } ^ { 5 } F d x = \int _ { 0 } ^ { 5 } \left( 7 - 2 x + 3 x ^ { 2 } \right) d x = [7x−x2+x3]05\left[ 7 x - x ^ { 2 } + x ^ { 3 } \right] _ { 0 } ^ { 5 }

= 35 – 25 + 125 = 135 J