Question
A particle moves along the x-axis from $x = 0$ to $x = 5m$ under the influence of a force given by $f(x) = 7 - 2x + 3x^2$. Calculate the work done.
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Answer
As work done, dW = Fdx $\text{W}=\int_\limits{0}^{5}\text{F}.\text{dx}=\int_\limits{0}^{5}(7-2\text{x}+3\text{x}^2)\text{dx}$
$=\bigg[7\text{x}-\frac{2\text{x}^2}{2}+\frac{3\text{x}^3}{3}\bigg]^5_0$ $=7(5-0)-(5^2-0)+(5^3-0)$ $=135\text{J}$
$=\bigg[7\text{x}-\frac{2\text{x}^2}{2}+\frac{3\text{x}^3}{3}\bigg]^5_0$ $=7(5-0)-(5^2-0)+(5^3-0)$ $=135\text{J}$
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