Question

If the speed of a vehicle increases by $2\text{m/s}$, its kinetic energy is doubled, then original speed of the vehicle is

• A. $\sqrt{2}+1\text{m/s}$
• B. $2(\sqrt{2}-1)\text{m/s}$
• C. $2(\sqrt{2}+1)\text{m/s}$
• D. $\sqrt{2}(\sqrt{2}+1)\text{m/s}$

Answer 1

The correct option is C $2(\sqrt{2}+1)\text{m/s}$

$K_f=2K_i$
$\frac{1}{2}m(v+2{)}^2=\left(\frac{1}{2}m{v}^2\right)(2)$
$v+2=\sqrt{2}v$
$v=\frac{2}{\sqrt{2}-1}=2(\sqrt{2}+1)\text{m/s}$