Find unit tangent vector vec$(T)(t)$ for the curve vec$(r)=($:$e^{-t}cost,e^{t}sint$:$)$

For the acceleration vec$(a)(t)=-32$hat$(j)$ and the given initial velocity vec$(v)(0)=600\sqrt[\phantom{2}]{3i}600$hat$(j)$ and the initial position vec$(r{)}_0=($:$0,0$:$)$ find the position of the object vec$(r)(t).$