Question

the accompanying graph shows the total distance s traveled by a bicyclist after t hours. using the graph answer parts (a) through (c) (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. 28 mph b. - 28 mph c. -27 mph d. 27 mph

Explanation:

Step1: Recall average - speed formula

The average speed formula is $v_{avg}=\frac{\Delta s}{\Delta t}$, where $\Delta s$ is the change in distance and $\Delta t$ is the change in time.

Step2: Calculate average speed for $[0,1]$

From the graph, at $t = 0$, $s=0$; at $t = 1$, $s = 12$. Then $\Delta s=12 - 0=12$ miles and $\Delta t=1 - 0 = 1$ hour. So $v_{avg}=\frac{12-0}{1 - 0}=12$ mph.

Step3: Calculate average speed for $[1,2.5]$

At $t = 1$, $s = 12$; at $t = 2.5$, $s=28$. Then $\Delta s=28 - 12 = 16$ miles and $\Delta t=2.5 - 1=1.5$ hours. So $v_{avg}=\frac{28 - 12}{2.5 - 1}=\frac{16}{1.5}=\frac{32}{3}\approx21.33$ (There is an error in the options provided. If we assume some reading - error from the graph and recalculate in a more approximate way, if we consider the closest value)

Answer:

(a) C. 12 mph
(b) None of the options are correct based on the correct calculation. If we assume some approximation error from graph - reading, the closest value to the calculated average speed is A. 28 mph (but this is not the exact value).