Question

An object is displaced from position vector $r_1=(2\hat{i}+3\hat{j})m$ to $r_2=(4\hat{i}+6\hat{j})m$ under a force $F=(3x^2\hat{i}+2y\hat{j})N$. Find the work done by this force.

Answer 1

Work done $W=\int \overrightarrow{F}.(dx\hat{i}+dy\hat{j})$

Work done $W={\int }_2^{4}3x^{2}dx+{\int }_3^{6}2ydy$

Or $W=x^3{|}_2^4+y^2{|}_3^6$

Or $W=4^3-2^3+6^2-3^2=85J$