Question

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

Answer 1

Since, the Force acting on the body is variable, this means we cannot directly use the formula,

Work = F.S

For the force to be variable, work should be calculated by the phenomenon of the Integration.

∴ Work = $\int\limits^3_0 {(5x^2 - 2x)} \, dx$

∴ Work = $\int\limits^3_0 {(5x^2)} \, dx - \int\limits^3_0 {(2x)} \, dx$

∴ Work = 5/3 × 3³ - 2/2 × 3²

⇒ Work = 45 - 9

∴ Work = 36 J.

Hope it helps .

Answer 2

Answer :-

Given ,

F= (5x²-2x)N.

The Force acting on the body is variable, this means we cannot directly use the formula,

Work = F.S

 ∫ dw =  ∫f.dx

= (5x²-2x) ×dx

= 5x²×dx -2x ×dx

= 5x^3/3 -2x²/2

= 5×27/3 -9

= 5×9-9

= 45-9

∴ Work = 36 J. Ans

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@GauravSaxena01