Question

christine is driving a racecar. the table below gives the distance d(t)

time t (seconds)	distance d(t) (meters)
2	71.2
4	166.4
6	172.8
10	239.6

(a) find the average rate of change for the distance driven from 0 seconds to 4 seconds.

meters per second

(b) find the average rate of change for the distance driven from 6 seconds to 10 seconds.

meters per second

Explanation:

Step1: Recall average - rate - of - change formula

The formula for the average rate of change of a function $y = f(x)$ from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, the function is $D(t)$ (distance as a function of time), and the average rate of change of distance with respect to time is the average speed.

Step2: Solve part (a)

For the time interval from $t = 0$ to $t = 4$ seconds, $a = 0$, $b = 4$, $D(0)=0$, and $D(4)=166.4$. Using the formula $\frac{D(4)-D(0)}{4 - 0}=\frac{166.4 - 0}{4}=\frac{166.4}{4}=41.6$.

Step3: Solve part (b)

For the time interval from $t = 6$ to $t = 10$ seconds, $a = 6$, $b = 10$, $D(6)=172.8$, and $D(10)=239.6$. Using the formula $\frac{D(10)-D(6)}{10 - 6}=\frac{239.6-172.8}{4}=\frac{66.8}{4}=16.7$.

Answer:

(a) 41.6
(b) 16.7