Question

A particle moves along the $x-$axis from $x=1\text{m}$ to $x=3\text{m}$ under the influence of a force $F=3x^2-2x+5$ newton acting along $x-$ axis. The work done in this process is

• A. $9\text{J}$
• B. $28\text{J}$
• C. $27\text{J}$
• D. zero

Answer 1

The correct option is B $28\text{J}$

Work done by a variable force is
$W={\int }_1^{3}F.dx={\int }_1^3(3x^2-2x+5)dx$
$=[x^3-x^2+5x{]}_1^3=[(27-9+15)-(1-1+5)]=28\text{J}$
Hence, the correct answer is option (b).