Question

Calculate the average rate of change in the graph from time t=0.5 to t=0.75. Include units on your final answer.

Answer 1

`\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} t_1=0.5\\ t_2=0.75 \end{cases}\implies \cfrac{f(0.75)-f(0.5)}{0.75 - 0.5}\implies \cfrac{7.744-6.275}{0.75-0.5} \\\\\\ \cfrac{1.469}{0.25}\implies 5.876~(meters)/(second)`