A particle moves along $X$-axis from $x=0$ to $x=5 \mathrm{~m}$ under the influence of force given b

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.....

Professor PC Thomas Classes · Answer

The given force varies with distance
Therefore, work done,
$$
\begin{aligned}
& W=\int_0^{x=5} F . d x \
& =\int_0^5\left(7-2 x+3 x^2ight) d x \
& =\left[7 x-\frac{2 x^2}{2}+\frac{3 x^3}{3}ight]_0^5 \
& =\left[7 	imes 5-(5)^2+(5)^3-0ight] \
& =135 \mathrm{~J}
\end{aligned}
$$