# Vector uses in physics – Calculate velocity and acceleration – Exercise 3866

Exercise

Given a vector radius of a point as a function of time

$$\vec{r}(t)=\vec{v_0}t-\frac{1}{2}gt^2\vec{k}$$

Where the initial velocity is

$$\vec{v_0}=\vec{v}(0)=(v_{01},v_{02},v_{03})$$

Calculate the velocity function, the acceleration function and their values (size).

$$\vec{v}(t)=(v_{01},v_{02},v_{03}-gt)$$

$$|\vec{v}(t)|=\sqrt{v^2_{01},v^2_{02},{(v_{03}-gt)}^2}$$

$$\vec{a}(t)=-g\vec{k}$$

$$|\vec{a}(t)|=g$$

### Solution

Coming soon…

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