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>> $A particle moves along the x - axis from$

Question

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

A

70

B

270

C

35

D

135

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Solution

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Correct option is D)

$w = \int F d x$
$= \int_{0}^{5} 7 - 2 x + 3 x^{2} d x$
$= [7 x - \frac{2 x ^{2}}{2} + \frac{3 x ^{2}}{3}]_{0}^{5}$
$= [7 x - x^{2} + x^{3}]_{0}^{5}$
$= [7 \times 5 - 5^{2} + 5^{3}] - [0 - 0 + 0]$
$= [35 - 25 + 125] - 0$
$= 135 J$
In this question, answer is 135 J not 70J

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