Answer all graph below represent a trip taken by bicycle. use the graph to answer questions

11. during the trip the cyclist stops for a time. during which labeled section-a, b, c, or d- did he stop?

12. during which labeled section was he traveling the slowest?

13. during which labeled section was he traveling the fastest?

14 calculate the speed of the cyclist during section d

15. how far away was the cyclist when he turned around and headed home?

Part 11) The cyclist stops for a time during the section B

Part 12) He traveling slowest in section A

Part 13) He traveling fastest in section C

Part 14) The speed in section D is 20 km/h

Part 15) The cyclist was 60 km from home when he turned around

Step-by-step explanation:

we know that

The speed is the ratio of the distance by the time

s=d/t

The slope of the graph is equal to the speed of the cyclist

Part 11. During the trip the cyclist stops for a time. During which labeled section-A, B, C, or D- did he stop?

The cyclist stops for a time during the section B

Because, during section B the distance is a constant (d=30 km)

therefore

The speed is equal to zero (Remember that the slope of a horizontal line is equal to zero)

Part 12. During which labeled section was he traveling the slowest?

Find the slope (speed) in each section

Find the slope in section A

Let

A(0,0) and B(4,30)

the slope is equal to

m=(30-0)/(4-0)=7.5 km/h

Find the slope in section B

Is a horizontal line

therefore

the slope is equal to

m=0 km/h

Find the slope in section C

Let

C(6,30) and D(7,60)

the slope is equal to

m=(60-30)/(7-6)=30 km/h

Find the slope in section D

Let

E(7,60) and F(10,0)

the slope is equal to

m=(0-60)/(10-7)=-20 km/h ---> is negative because in this section he turned around

therefore

He traveling slowest in section A

Part 13. During which labeled section was he traveling the fastest?

Remember part 12)

Slope in section C

Let

C(6,30) and D(7,60)

the slope is equal to

m=(60-30)/(7-6)=30 km/h > is the greater slope

therefore

He traveling fastest in section C

Part 14. Calculate the speed of the cyclist during section D

Remember part 12)

Slope in section D

Let

E(7,60) and F(10,0)

the slope is equal to

m=(0-60)/(10-7)=-20 km/h ---> is negative because in this section he turned around

therefore

The speed in section D is 20 km/h

Part 15. How far away was the cyclist when he turned around and headed home

Observing the graph

we know that the cyclist turned around at point (7,60)

therefore

The cyclist was 60 km from home when he turned around