Question

A particle moves along the x-axis from $x=0$ to $x=5m$ under the influence of a force $F$ (in N) given by $F=3x^2-2x+7$. Calculate the work done by this force

Answer 1

The work done in moving the particle from $x=0$ to $x=5$ is given by,

$W=\int dW=\int Fdx$

$W={\int }_0^5({3x}^2-2x+7)$

On integrating

$W={[\frac{3x^3}{3}-\frac{2x^2}{2}+7x]}_0^5$

$W=[5^3-5^2+7\times 5]-0$

$W=125-25+35$

$W=135J$