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. $2(\sqrt{2}-1)$ m/s
• C. $2(\sqrt{2}+1)$ m/s
• D. $\sqrt2(\sqrt{2}+1)$ m/s

Answer 1

Answer: (C)

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

Answer 2

The correct option is C)
Let the initial speed of the vehicle be v $\frac{m}{s}$
According to the question :
2 ($\frac{mv^2}{2}$) = $\frac{m(v+2)^2}{2}$
$v^2=4+4v$
$v^2-4v-4=0$
v = 2($\sqrt2$+1) $\frac{m}{s}$