Explanation:
more proper to say that mass is equivalent to energy as per Einstein's [math]E=mc^2[/math], and that energy changes according to speed as:
[math]E=\dfrac{m_0c^2}{\sqrt{1-\frac{v^2}{c^2}}}[/math]
where [math]m_0[/math] is the intrinsic mass of the object (sometimes called the rest mass). When you expand this as an infinite series, everything after the first two terms drops out when [math]\frac{v}{c}\to 0[/math] (the classical limit), leaving you with [math]E=m_0c^2+½m_0v^2[/math].
In other words, the energy change according to speed is none other than the object's kinetic energy.