A body of mass $m$ is accelerated uniformly from rest to a speed $v$ in a time $T$. The instantaneous power delivered to the body as a function time is given by\\
(1) $\frac{mv^2}{T^2} \cdot t$\\
(2) $\frac{mv^2}{T^2} \cdot t^2$\\
(3) $\frac{1}{2}\frac{\mathrm{mv}^2}{\mathrm{T}^2} \cdot \mathrm{t}$\\
(4) $\frac{1}{2}\frac{\mathrm{mv}^2}{\mathrm{T}^2} \cdot \mathrm{t}^2$