Instructions

The program in Example $8-7$ outputs the average speed over the intervals of length $10.$ Modify the program so that the user can store the distance traveled at the desired times, such as times $0,10,16,20,30,38,$ and $45.$ The program then computes and outputs the average speed of the object over the successive time intervals specified by the time when the distance was recorded. For example, for the previous list of times, the average speed is computed over the time intervals $0$ to $10,16$ to $20,20$ to $30,30$ to $38,$ and $38$ to $45.$

Instructions for Example $8-7$ have been included for your convenience.

Example $8-7$

Suppose that the distance traveled by an object at time t $=$ a$1$ is d$1$ and at time t $=$ a$2$ is d$2,$ where a$1<$ a$2.$ Then the average speed of the object from time a$1$ to a$2,$ that is$,$ over the interval $[$a$1,$ a$2]$ is $($d$2-$ d$1)($a$2-$ a$1).$ Suppose that the distance traveled by an object at certain times is given by the following table:

Time Distance

$00$

$1018$

$2027$

$3038$

$4052$

$5064$

Then the average speed over the interval $[0,10]$ is $(18-0)/(10-0)=1\mathrm{.}8,$ over the interval $[10,20]$ is $(27-18)/(20-10)=0\mathrm{.}9,$ and so on$.$

An example of the program is shown below:

Enter time and the distance traveled at that time $0$

$0$

Enter time and the distance traveled at that time $10$

$18$

Enter time and the distance traveled at that time $20$

$27$

Enter time and the distance traveled at that time $30$

$38$

Enter time and the distance traveled at that time $40$

$52$

Enter time and the distance traveled at that time $50$

$64$

$00\mathrm{.}00$

$1018\mathrm{.}00$

$2027\mathrm{.}00$

$3038\mathrm{.}00$

$4052\mathrm{.}00$

$5064\mathrm{.}00$

Time Distance Traveled Average Speed $/$ Time Interval

$00\mathrm{.}000[0,0]$

$1018\mathrm{.}001\mathrm{.}80[0,10]$

$2027\mathrm{.}000\mathrm{.}90[10,20]$

$3038\mathrm{.}001\mathrm{.}10[20,30]$

$4052\mathrm{.}001\mathrm{.}40[30,40]$

$5064\mathrm{.}001\mathrm{.}20[40,50]$