Kinetic energy is given by $k = \dfrac{1}{2}mv^2$. For a constant mass, there is approximately 1% increase in energy. Find the increase in velocity v which causes this increase in energy.
$k = \dfrac{1}{2}mv^2$
$\therefore$ $\dfrac{dk}{dv}=mv$
$\Delta k = 1\% \text{ of k}=0.01 \times \dfrac{1}{2}mv^2 = 0.005 mv^2$
Now, $\Delta k = \left(\dfrac{dk}{dv}\right) \times \Delta v$
$\therefore$ $\Delta v = \dfrac{\Delta k}{dk / dv}= \dfrac{0.005 mv^2}{mv} = 0.005 v$
i.e. velocity increases by $0.5 \%$