Vector uses in physics – Calculate motion – Exercise 3874

Exercise

Particle acceleration depends on time according to the acceleration formula

$$\vec{a}(t)=18\cos(3t)\vec{i}-18\sin(3t)\vec{j}$$

The initial vector radius of the particle is

$$\vec{r}(0)=(2,0,1)$$

And the initial velocity of the particle is

$$\vec{v}(0)=(0,2,4)$$

Calculate the equation of motion of the particle.

$$\vec{r}(t)=(-2\cos(3t)+4)\vec{i}+(2\sin(3t)-4t)\vec{j}+(4t+1)\vec{k}$$