## Calculus (3rd Edition)

$$v(1)=\sqrt{74}.$$
Since $r(t)=\lt t^3, 1-t, 4t^2\gt$, then the velocity vector is given by $$r'(t)=\lt 3 t^2, -1, 8t\gt$$ and the acceleration vector is given by $$r''(t)=\lt 6 t, 0, 8\gt.$$ Moreover, the speed at $t=1$ is $$v(1)=\|r'(1)\|=\sqrt{9+1+64}=\sqrt{74}.$$