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A body of mass 0.5 kg travels in a straight line with velocity $v = 5 x^{3 / 2} m / s .$ The work done by the net force during the displacement from $x = 0$ to $x = 2 m$

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75 J

50 J

100 J

25 J

answer is B.

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Detailed Solution

$At x = 0, v_{i} = 5 {(0)}^{3 / 2} = 0$

$and x = 2 m, v_{f} = 5 {(2)}^{3 / 2} = 5 \sqrt{8} m/s$

$W = Δ K$

$= \frac{1}{2} m (v_{f}^{2} - v_{i}^{2}) = \frac{1}{2} x 0.5 [{(5 \sqrt{8})}^{2} - 0^{2}] = 50 J$

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