A student is given a position function $x\left(t\right)$ and wants to obtain the acceleration function $a\left(t\right)$. Which operation sequence is correct?

A cart moves along a track with position $x\left(t\right)=2t^3-9t^2+4t+1$, where $x$ is in meters and $t$ is in seconds. What is its acceleration at $t=2$ $\text{s}$?

The acceleration of a test vehicle is $a\left(t\right)=4t+1$ in ${\text{m/s}}^2$. What is the change in velocity from $t=1$ $\text{s}$ to $t=3$ $\text{s}$?

A glider has acceleration $a\left(t\right)=4t+6$, initial velocity $v\left(0\right)=-2$ $\text{m/s}$, and initial position $x\left(0\right)=3$ $\text{m}$. Which position function $x\left(t\right)$ describes the motion?

Which statement correctly distinguishes average acceleration from instantaneous acceleration?