A particle moves along the x-axis from x = 0 to x = 5 m under the influence of a force given by f = 5 2x + 3x2 n. The work done in this process is
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Given: A particle moves along the x-axis from x = 0 to x = 5 m under the influence of a force given by f = 5 - 2x + 3x2 .
To find: the work done in the process.
Solution: For variable force, we know that work done is given by:
∫dW = ∫F.ds
Putting the given values in the formula, we get:
∫dW = ∫⁵₀ (3x² - 2x + 5) dx
= 3(x³/3)⁵₀ - 2(x²/2)⁵₀ + 5(x)⁵₀
= 125 - 25 + 25
= 125 J
Hence, the work done in the process is 125 J.
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