A particle moves along the x-axis from x=0 to x=5 m under the influence of a force given by F= 7 - 2x + 3x2 . The work done in the process is-

Question

A particle moves along the x-axis from x=0 to x=5 m under the influence of a force given by F= 7 - 2x + 3x2 . The work done in the process is- (A) 70J (B) 270J (C) 35J (D) 135J

Tardigrade Admin · Accepted Answer

W= displaystyle ∫ F.dx= displaystyle ∫ 05 (. 7 - 2 x + 3 x2 .) dx =[7 x - (2 x2/2) + (3 x3/3)]05 =35-25+125=135 J

Q. A particle moves along the x-axis from $x = 0$ to $x = 5 m$ under the influence of a force given by $F = 7 - 2 x + 3 x^{2}$ . The work done in the process is-

$70 J$

$270 J$

$35 J$

$135 J$

$W = \int F . d x = \int_{0}^{5} (7 - 2 x + 3 x^{2}) d x$
$= [7 x - \frac{2 x ^{2}}{2} + \frac{3 x ^{3}}{3}]_{0}^{5}$
$= 35 - 25 + 125 = 135 J$

Q. A particle moves along the x-axis from x=0 to x=5m under the influence of a force given by F=7−2x+3x2 . The work done in the process is-

70J

270J

35J

135J