Question

A block of mass 10 kg, moving in x direction with a constant speed of 10 $m{s}^{-1}$, is subjected to a retarding force F = $0.1xJ/m$ during its travel from x = 20 m to 30 m. Its final KE will be:

Answer 1

Work done $W=\int F.dx={\int }_{20}^{30}-0.1xdx$

Or $W=-0.1\times \frac{x^2}{2}{|}_{20}^{30}=-0.1\times \frac{({30}^2-{20}^2)}{2}=-25J$

Work done $W=K.E_f-K.E_i$

Or $-25=K.E_f-\frac{1}{2}m{u}^2$

Or $-25=K.E_f-\frac{1}{2}\times 10\times {10}^2$

$⟹K.E_f=475J$