Question

If the speed of a vehicle increases by $2m/s$, its kinetic energy is doubled. Then, the original speed of the vehicle is:

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

Answer 1

Answer: (C)

$2(\sqrt{2}+1)m/s$

Let original speed of the vehicle is $v$

$\frac{1}{2}m(v+2{)}^2=2\left(\frac{1}{2}m{v}^2\right)$

$v+2=\sqrt{2}v\Rightarrow (\sqrt{2}-1)v=2$

$\Rightarrow v=\frac{2}{\sqrt{2}-1}\times \frac{\sqrt{2}+1}{\sqrt{2}+1}=2(\sqrt{2}+1)$