Vector uses in physics – Calculate angle between velocity vector and acceleration vector – Exercise 3878

Exercise

Calculate the angle between the velocity and acceleration vectors at t = 0 if the motion vector is

$$\vec{r}(t)=\ln(t^2+1)\vec{i}+\arctan t\vec{j}+\sqrt{t^2+1}\vec{k}$$

$$\alpha=\frac{\pi}{2}$$