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(A) Let the position vector of a particle be $\vec{r}(t)$.$1$. The first differentiation of the position vector with respect to time $t$ gives the vel

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Velocity and Acceleration

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(A) Let the position vector of a particle be $\vec{r}(t)$.$1$. The first differentiation of the position vector with respect to time $t$ gives the velocity vector:$\vec{v} = \frac{d\vec{r}}{dt}$$2$. The second differentiation of the position vector with respect to time $t$ (or the first differentiation of velocity) gives the acceleration vector:$\vec{a} = \frac{d\vec{v}}{dt} = \frac{d^2\vec{r}}{dt^2}$Therefore,the first differentiation gives velocity and the second differentiation gives acceleration.

$t (s)$	$0$	$1$	$2$	$3$
$x (m)$	$-2$	$0$	$6$	$16$

Which physical quantity can be found by first differentiation and second differentiation of position vector?

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