Work Energy Theorem

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Question

A block of mass 5 kg is moving in x-direction with a constant speed of 10 m/s. it is subjected to a retarding force $F = (- 0.2 x) N$ during its travel from x=20 m to x=30 m. its final kinetic energy will be

Moderate

Solution

$\begin{array}{l} According to Work-Energy theorem \\ K_{f} - K_{i} = W \\ K_{f} = K_{i} + W \\ = \frac{1}{2} \times 5 \times 10^{2} + \int_{20}^{30} (- 0.2 x) d x \\ =200 J \end{array}$

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