Question

If a force f = (2x + 3x2 )î n acts along x-axis on an object and moves it from x = 2î m to x = 4î m, the work done is

Answer 1

Work done is the dot product of force vector and displacement vector
e.g., W = $\overrightarrow{F}.\overrightarrow{S}$

Here given ,
F = (2x + 3x²)i , here we see F is variable so, we have to use integration
So, work done , W = $\bold{\int\limits^{x_2}_{x_1}{F(x)}\,dx}$
W = $\bold{\int\limits^4_2{(2x + 3x^2)}\,dx}$
= $\bold{\int\limits^4_2{(2x )}\,dx +\int\limits^4_2{3x^2}\,dx}$
= $\bold{\frac{2}{2}[x^2]^4_2+\frac{3}{3}[x^3]^4_2}$
= (16 - 4) + (64 - 8)
= 12 + 56
= 68 J

Hence, answer is 68J