Question

answer these questions about the graph on the above:
a. how many total miles did the car travel?
b. what was the average speed of the car for the trip? (hint: total
c. describe the motion of the car between hours 5 and 12?
d. what is happening between points c and d?
e. how many miles were traveled in the first two hours of the trip?
f. between which two points is the fastest speed?

Explanation:

Step1: Find total miles

From the graph, the car ends at 150 miles on the y - axis. So the total miles traveled is 150 miles.

Step2: Calculate average speed

Average speed = $\frac{\text{Total distance}}{\text{Total time}}$. Total distance is 150 miles and total time is 20 hours. So average speed = $\frac{150}{20}=7.5$ miles per hour.

Step3: Describe motion between 5 - 12 hours

Between 5 and 12 hours, the y - value (miles) is constant at 50 miles. So the car is stationary.

Step4: Find miles between C and D

At point C, the y - value is 50 miles and at point D, the y - value is 0 miles. So the miles traveled between C and D is $50 - 0=50$ miles.

Step5: Find miles in first 2 hours

At 2 hours, the y - value is approximately 25 miles. So 25 miles were traveled in the first 2 hours.

Step6: Determine fastest speed

The steepest part of the graph represents the fastest speed. The section between points E and F has the steepest slope.

Answer:

a. 150 miles
b. 7.5 miles per hour
c. The car is stationary.
d. 50 miles
e. 25 miles
f. Between points E and F.