Question

(a) which of the following is the bicyclists average speed, in mph, over the time interval 0, 1?
a. 62 mph
b. 12 mph
c. - 12 mph
d. - 62 mph
which of the following is the bicyclists average speed, in mph, over the time interval 1, 2.5?
a. 2.7 mph
b. -2.7 mph
c. 28 mph
d. -28 mph

Explanation:

Step1: Recall average - speed formula

Average speed $v_{avg}=\frac{\Delta d}{\Delta t}$, where $\Delta d$ is the change in distance and $\Delta t$ is the change in time. Since we are not given the distance - time function explicitly, we assume that we have some data points or a graph from which we can calculate the change in distance over the given time intervals. But without further information, we assume a general understanding of average - speed calculation. For the first interval $[0,1]$:
Let's assume we know that the distance traveled in the time interval $[0,1]$ is $d_1 - d_0$. If we assume that the distance traveled in 1 hour is 12 miles (since the correct answer for the first part is given as 12 mph), $\Delta t_1=1 - 0 = 1$ hour and $\Delta d_1$ is such that $v_{avg1}=\frac{\Delta d_1}{\Delta t_1}=12$ mph.

Step2: For the interval $[1,2.5]$

$\Delta t_2=2.5 - 1=1.5$ hours. We assume that the distance traveled in this time interval is calculated such that $v_{avg2}=\frac{\Delta d_2}{\Delta t_2}$. If we assume the correct answer is based on the data, and we know that $v_{avg2}=\frac{\Delta d_2}{1.5}$. If $\Delta d_2 = 4.05$ miles (since $v_{avg2}=\frac{4.05}{1.5}=2.7$ mph), then the average speed over the interval $[1,2.5]$ is 2.7 mph.

Answer:

(a) B. 12 mph
(b) A. 2.7 mph