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# The displacement (in feet) of a particle moving in a straight line is given by $s = \frac{1}{2}t^2 - 6t + 23$, where $t$ is measured in seconds.(a) Find the average velocity over each time interval: (i) $[4, 8]$ (ii) $[6, 8]$ (iii) $[8, 10]$ (iv) $[8, 12]$ (b) Find the instantaneous velocity when $t = 8$.(c) Draw the graph of $s$ as a function of $t$ and draw the secant lines whose slopes are the average velocities in part (a). Then draw the tangent line whose slope is the instantaneous velocity in part (b).

## a) see solutionb) 2 $\mathrm{ft} / \mathrm{s}$c) see graph

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