Answer
$|a|=5.31$ m/s$^2$
$\alpha=\cos^{-1}(0.6022)=53^{\circ}$
$\beta=\cos^{-1}(0.7984)=37^{\circ}$
$\gamma=\cos^{-1}(0)=90^{\circ}$
Work Step by Step
$v(t)=0.8t^2 i + 12t^{1/2} j + 5 k$
$a=\frac{dv}{dt}=1.6t i + 6t^{-1/2} j$
When $t=2$ s, $a=3.2i + 4.243j$
$|a|=\sqrt{(3.2)^2+(4.243)^2}=5.31$ m/s$^2$
$u_o=\frac{a}{|a|}=0.6022i+0.7984j$
$\alpha=\cos^{-1}(0.6022)=53^{\circ}$
$\beta=\cos^{-1}(0.7984)=37^{\circ}$
$\gamma=\cos^{-1}(0)=90^{\circ}$
