Question

A block of mass 10 kg is moving in x-direction with a constant speed of 10 m/sec. It is subjected to a retarding force F = 0.1 x joule/metre during its travel from x = 20 metre to x = 30 metre. Its final kinetic energy will be

• A. 475 joule
• B. 450 joule
• C. 275 joule
• D. 250 joule

Answer 1

The correct option is A 475 joule

We know that,
Change in kinetic energy = work done on the object by force
Here, work done $\int Fdx={\int }_{20}^{30}0.1xdx$
$=0.1{\left[\frac{x^2}{2}\right]}_{20}^{30}=\frac{0.1}{2}[{30}^2-{20}^2]$
$=0.05[900-400]=0.05\times 500=25$ joule
Now, initial kinetic energy
$=\frac{1}{2}\times 10\times 100=500$ joule
Final kinetic energy = 500 -25 = 475 joule
[Direction of force is opposite to direction of motion]