91影视

Mass of block is$m=6.00鈥�\mathrm{kg}$

Distance travelled by block is$14.0鈥�\text{m}$

Energy cannot be created or destroyed; it can only be transformed from one form into another or transferred from one object to another, according to the physical rule of conservation of energy.

Firstly determine the work done and it is given as

$W={鈭�}_{x=0}^{x=14}F\left(x\right)dx$

Substitute all the value in above equation to get the value of work done

$\begin{array}{rcl}W& =& {鈭�}_{x=0}^{x=14}\left(18.0鈥�\text{N}-(0.530鈥�\text{N/m)}x\right)dx\\ & =& {\left[\left(18.0鈥�\text{N}\right)鈥�x-(0.530鈥�\text{N/m)}\frac{x^2}{2}\right]}_{x=0}^{x=14}\\ & =& 200.06鈥�\text{J}\end{array}$

This work done will be equal to the change in kinetic energy by the law of energy conservation, so

$W=\frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2$ ...(i)

Where $u$is initial velocity and is the final velocity

It is given in the question that the initial velocity is zero so the initial velocity$u=0$

Substitute all the values in equation (i)

$\begin{array}{rcl}200.06鈥�\text{J}& =& \frac{1}{2}鈥�脳6鈥�\text{kg}脳v^2\\ v& =& 8.17鈥�\text{m/s}\\ & & \end{array}$

Hence the speed is$8.17鈥�\text{m/s}$