The position function for a particle moving on the $x$-axis is $x\left(t\right)=-2t^2+18t+7$. What is the particle's initial velocity?

The position of a small object is given by $x=0.6e^{2t}-1$, where $t$ is in seconds and $x$ in meters. At what time is the small object travelling with a velocity $v=65.5\text{ m/s}$?

A ball's velocity is given by $v\left(t\right)=\frac{1}{2}{t}^3-2t$. Calculate the ball's displacement from $t=1.5s$ to $t=3s$.