# The average speed of the man between 68 s and 152 s. ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2.4, Problem 26E

(a)

To determine

## To find: The average speed of the man between 68 s and 152 s.

Expert Solution

The average speed of man between 68 s and 152 s is 4.76 m/s.

### Explanation of Solution

Given:

The given table is,

 Time(s) Distance(m) 32 200 68 400 108 600 152 800 203 1,000 263 1,200 335 1,400 412 1,600

Formula used:

Average rate of change of function y=f(x) between x=a and x=b is given by,

Averagerateofchange=ChangeinyChangeinx=f(b)f(a)ba (1)

Calculation:

The table shows the record of the time taken by man while running at the end of each lap.

From the given table the distance covered by the runner at 68 s is 400 and at time 152 s is 800.

Substitute f(a)=400, f(b)=800, a=68 and b=152 in equation (1).

Averagerateofchange=80040015268=40084=4.76m/s

Therefore, average speed of man between 68 s and 152 s is 4.76 m/s.

(b)

To determine

### To find: The average speed of the man between 263 s and 412 s.

Expert Solution

The average speed of man between 263 s and 412 s is 2.68 m/s.

### Explanation of Solution

Calculation:

From the given table the distance covered by the runner at 263 s is 1,200 and at time 412 s the distance covered is 1,600.

Substitute f(a)=1,200, f(b)=1,600, a=263 and b=412 in equation (1).

Averagerateofchange=1,6001,200412263=400149=2.68m/s

Therefore, average speed of man between 263 s and 412 s is 2.68 m/s.

(c)

To determine

### To Calculate: The speed of man for each lap and to examine whether he is slowing down, speeding up, or neither.

Expert Solution

The man is slowing down after each lap.

### Explanation of Solution

Formula used:

speed=distancetravelled(m)timetaken(s) (1)

Calculation:

Substitute time taken to travel and distance of each lap that is 200 m in equation (1), and calculate speed for each lap.

Form a table with all these speeds along with the time and distance.

 Time(s) Distance(m) speed=distance travelled(m)time taken(s) 32 200 6.25 68 400 5.88 108 600 5.55 152 800 5.26 203 1,000 4.92 263 1,200 4.56 335 1,400 4.179 412 1,600 3.88

Table

From the table it can be observed that the speed of the man is decreasing after each lap.

Therefore, the man is slowing down.

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