Question

A particle moves along x-axis under the action of a position dependent force F = (5x2 - 2x) N. Work done by
forces on the particle when it moves from origin to x = 3 m is
(1) 45J
(2) 36 J
(3) 32J
(4) 42 J​

Answer 1

Here is your answer ,I hope it will help you

Answer 2

Work done by  the forces on the particle when it moves from origin to x = 3 m is 36J .

Option - 2

Explanation:

To get the correct answer we need to integrate the equation that is given to us and have to set the ranges from 0 to 3.

⨑F = ⨑ 5$x^2$ - 2x {from 0 to 3}

on integration of the above given equation we get the result  

= $\frac{(5x^3)}{3} - \frac{(2x^2)}{2}$

{In place of exporting the values of range 0 and 3 and then again solving the equation we get}

⇒ $\frac{5 \times 3^3}{3} - \frac{5 \times 0^3}{3} - \frac{2\times 3^2}{2} - \frac{2 \times 0^2}{2}$

⇒$5\times 3 \times 3 - 3^2$

⇒ 45-9 = 36J

Work done by  the forces on the particle when it moves from origin to x = 3 m is 36J .

To know more;

A particle moves along x-axis under the action of a position dependent force f is equal to (5x²-2x)N. work done by the force on the particle when it moves from origin to x is equal to 3 m  is

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