Question

A force $\overrightarrow{F}=(3x^2+2x-7)N$ acts on a 2 kg body as a result of which the body gets displaced from x=0 to x=5m. The work done by the force will be-

• A. 35 J
• B. 70 J
• C. 115 J
• D. 270 J

Answer 1

The correct option is C 115 J

Given,

$F=(3x^2+2x-7)N$

$m=2kg$

From x=0 to x=5m

The work done by the force will be,

$dW=F.dx$

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

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

$W=|x^3+x^2-7x{|}_0^5$

$W=(5{)}^3+(5{)}^2-7\left(5\right)$

$W=150-35$

$W=115J$

The correct option is C.