Textbook Problem

The displacement (in meters) of an object moving in a straight line is given by $s=1+2t+\frac{1}{4}{t}^2$, where $t$ is measured in seconds.

(a) Find the average velocity over each time period.

(i) $\left[1,3\right]$

(ii) $\left[1,2\right]$

(iii) $\left[1,1.5\right]$

(iv) $\left[1,1.1\right]$

(b) Find the instantaneous velocity when $t=1$.