Final K.E. under retarding force – Rankers Physics

Work Done by Constant and Variable Forces: Practice Problem & Solution

A block of mass $10\text{ kg}$ moving in $x$ direction with a constant speed of $10\text{ m s}^{-1}$, is subjected to a retarding force $F = -0.1x\text{ J/m}$ during its travel from $x = 20\text{ m}$ to $30\text{ m}$. Its final K.E. will be: (2015)
$450\text{ J}$
$275\text{ J}$
$250\text{ J}$
$475\text{ J}$

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Work Done by Constant and Variable Forces. Understanding the underlying formula is key to arriving at the correct answer below:

Use work-energy theorem: $K_f - K_i = W$. Initial kinetic energy is $K_i = \frac{1}{2}mv^2 = 500\text{ J}$. Work done by the force is $W = \int_{20}^{30} (-0.1x) dx = -25\text{ J}$. Thus, final kinetic energy is $K_f = 500 - 25 = 475\text{ J}$.

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