# Vector uses in physics – Calculate motion – Exercise 3868

Exercise

Particle velocity varies by the velocity function

$$\vec{v}(t)=2\vec{i}-\vec{j}-10t\vec{k}$$

At t = 0 the particle is at the point

$$\vec{r}(0)=(0,0,100)$$

Calculate the equation of motion of the particle.

$$\vec{r}(t)=2t\vec{i}-t\vec{j}-(5t^2+100)\vec{k}$$