Question

On the topic of Forces and Motion, what is a velocity and acceleration vector?

Answer 1

Let $\mathbf{r}$ be the radius vector of a point. Then by definitio, the velocity vector is the derivative of $\mathbf{r}$ with respect to time:

$$\mathbf{v} \equiv \dfrac{d\mathbf{r}}{dt}$$

The acceleration vector, by definition, is the derivative of $\mathbf{v}$ with respect to time:

$$\mathbf{a} \equiv \dfrac{d\mathbf{v}}{dt} = \dfrac{d^2\mathbf{r}}{dt^2}$$