A force F = (3x + 4) newton displaces an object of mass 10 kg from x = 0 to x = 4m. If the speed of the object at x = 0 is 2ms^-1, its speed at x = 4m will be ___m/s

Work done by the force is

$\begin{array}{l}\mathrm{dW}=\mathrm{fdx}\\ W={\int }_0^4 (3\mathrm{x}+4)\mathrm{dx}\\ ={\left|\frac{3{\mathrm{x}}^2}{2}+4\mathrm{x}\right|}_0^4=40\mathrm{J}\end{array}$

From work energy principle, work done = change in kinetic energy.

$\begin{array}{l} \mathrm{W}=\mathrm{\Delta k}=\frac{1}{2}\mathrm{m}\left({\mathrm{v}}^2-{\mathrm{u}}^2\right)\\ 40=\frac{1}{2}\times 10\times \left({\mathrm{v}}^2-2^2\right)\\ \Rightarrow \mathrm{v}=2\sqrt{3}=3.46{\mathrm{ms}}^{-1}\end{array}$