Question

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

• A. $\sqrt{95}m/s$
• B. $\sqrt{75}m/s$
• C. $10m/s$
• D. $7m/s$

Answer 1

The correct option is A $\sqrt{95}m/s$

Given that Mass of the block, $m=10kg$

It is moving in the x-direction

Initial speed of the block , $v_1=10m/s$

Force on the block , $F=-0.1x$

Let $v_2$ be the final velocity

We know that $F=mv\frac{dv}{dx}=-0.1x$

$⟹10vdv=-0.1xdx$

Integrating both sides we get:

$⟹10{\int }_{10}^{v_2}vdv=-0.1{\int }_{20}^{30}xdx$

$⟹10{\left(\frac{v^2}{2}\right)}_1^{V_2}0=-0.1{\left(\frac{x^2}{2}\right)}_{20}^{30}$

$⟹10(\frac{v_2^2}{2}-50)=-0.1(450-200)$

$⟹v_2=\sqrt{95}m/s$

So, final velocity of the block, $v_2=\sqrt{95}m/s$