Work done by Diff type of forces

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Question

A block of mass l0 kg moving in x direction with a constant speed of l0 ${ms}^{- 1}$ is subjected to a retarding force $F = 0.1 x J / m$ during its travel from x = 20 m to 30 m. Its final KE will be

Moderate

Solution

Using work--energy theorem, $W_{total} = ∆ K$
$W = \frac{1}{2} m (v^{2} - u^{2})$
$\Rightarrow \frac{1}{2} {mv}^{2} = W + \frac{1}{2} {mu}^{2}$
$W = \int_{20}^{30} F . dx = \int_{20}^{30} 0.1 . x . dx$
= ${-0.1∫}_{20}^{30} x dx + \frac{1}{2} \times 10 \times 10^{2}$
= -25 J + 500 J = 475 J

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