Question

maya is driving a racecar. the table below gives the distance ( d(t) ) (in meters) she has driven at a few times ( t ) (in seconds) after she starts.

(a) find the average rate of change for the distance driven from 0 seconds to 5 seconds.

( square ) meters per second

(b) find the average rate of change for the distance driven from 7 seconds to 9 seconds.

( square ) meters per second

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) over the interval \([x_1,x_2]\) is \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}\).

Step2: Solve part (a)

For the interval from \(t_1 = 0\) to \(t_2=5\), \(D(t_1)=0\) and \(D(t_2) = 151.5\).
Using the formula \(\frac{D(t_2)-D(t_1)}{t_2 - t_1}=\frac{151.5 - 0}{5-0}=\frac{151.5}{5}=30.3\)

Step3: Solve part (b)

For the interval from \(t_1 = 7\) to \(t_2 = 9\), \(D(t_1)=205.1\) and \(D(t_2)=255.9\)
Using the formula \(\frac{D(t_2)-D(t_1)}{t_2 - t_1}=\frac{255.9 - 205.1}{9 - 7}=\frac{50.8}{2}=25.4\)

Answer:

a) \(30.3\) meters per second
b) \(25.4\) meters per second