1.

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»

Work DONE is the dot product of force vector and displacement vector
e.g., W = F.S

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

Hence, ANSWER is 68J


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