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Answer :
The graph of the distance traveled by the car to the time taken during the 8 hours along the straight road gives;
11. The rates of change between the following times, t, are;
- t = 0 and t = 2 the rate of change is 30 mph
- t = 2 and t = 3 the rate of change is 60 mph
- t = 3 and t = 4 the rate of change is 0 mph
- t = 4 and t = 8 the rate of change is -30 mph
12. The car is not moving between times 3 and 4 hours
13. The car is traveling to the right between times 0 and 3 hours
14. The car is traveling to the left between times 4 and 8 hours
15. The car is traveling fastest between times 2 and 3 hours
What is a distance–time graph?
A distance–time graph is one that shows the variation of the distance traveled with respect to time, such that a positive distance traveled indicates a forward distance and a negative distance traveled indicates reversed motion.
The points on the graph in the possible question obtained online are;
(0, 0), (2, 60), (3, 120), (4, 120), (8, 0)
From the above points, the attached graph is constructed using Sheets
11. The rates of change in distance with respect to time are;
- [tex] \displaystyle { \frac{ (\triangle d)_{1} }{ \triangle t} = \frac{60 - 0}{2 - 0} = 30}[/tex]; Velocity = 30 mph
- [tex] \displaystyle { \frac{ (\triangle d)_{2} }{\triangle t} = \frac{120 - 60}{3 - 2} = 60}[/tex]; Velocity = 60 mph
- [tex] \displaystyle { \frac{ (\triangle d)_{3} }{\triangle t} = \frac{120 - 1200}{4 - 3} = 0}[/tex]; Velocity = 0 mph
- [tex] \displaystyle { \frac{ (\triangle d)_{4} }{\triangle t} = \frac{0 - 120}{8 - 4} = - 30}[/tex]; Velocity= -30 mph
12) When the car is not moving, we have that the rate of change of distance with time is zero, that is the car's distance does not change with time.
The two times between which the car is not moving is between the 3 hour and 4 hour points on the graph
13. The velocity of the car is given by the rate of change of the distance with time of the car
The positive rate of change on the graph is given between the times 0 and 3 hours after the car starts motion.
The car is traveling to the right between times, t = 0 and t = 3
14. The car has negative rate of change and therefore, negative velocity, and therefore also the car is moving to the left between times, t = 4 hours, and t = 8 hours
15. The car is traveling fastest when the rate of change of the car's distance traveled with time is highest, which is given by the times between t = 2 hours and t = 3 hours in which the car is traveling at 60 miles per hour
Learn more about distance time graph here;
https://brainly.com/question/13877898
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