Q: A body of mass 8 kg is moved by a force F = (3x)N, where x is the distance covered. Initial position is x = 2 m and final position is x = 10 m. If initially the body is at rest, find the final speed.
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Sol: F = ma
$\large F = m v\frac{dv}{dx}$
$\large 3 x = 8 v\frac{dv}{dx}$
$\large \int_{2}^{10} 3 x dx = \int_{0}^{v} 8 v dv $
$\large 3 [\frac{x^2}{2}]_{2}^{10} = 8[\frac{v^2}{2}]_{0}^{v} $
$\large v^2 = \frac{3 \times 96}{8} = 36 $
v = 6 m/s