Question

physical science
understanding motion: using graphs to illustrate distance and time
name
date
using graphs to illustrate distance and time
in science, data is often plotted on a graph. data relating to speed and velocity are often plotted on special graphs that show specific relationships.
one such graph for plotting information related to speed is a distance/time graph. the distance/time graph below shows the distance one might travel by train, plane, and bicycle for different times.
refer to the distance/time graph and answer the following questions. circle the correct answer and/or fill in the blank.

1. the airplane has traveled (a) 100 (b) 150 (c) 200 miles in (d) ____ hours.
2. the automobile has traveled (a) 75 (b) 100 (c) 200 miles in (d) ____ hours.
3. the line representing the distance traveled by a bicycle would likely be (a) line a (b) line b.
4. the airplane is averaging ____ miles per hour.
5. the automobile is averaging ____ miles per hour.
6. extend the line for the airplane to show where the line will end after the plane has flown 1 1/2 hours.
7. after completing #6, the airplane will have traveled a total of ____ miles.
8. extend the line for the automobile to show where the line ends after the car has traveled another 3 hours.
9. after completing #8, the automobile will have traveled a total of ____ miles.

Explanation:

Step1: Find airplane distance at 0.5 hours

From the graph, at 0.5 hours, airplane is at 100 miles.

Step2: Find automobile distance at 8 hours

From the graph, automobile reaches 200 miles at 8 hours.

Step3: Identify bicycle line

Bicycle is slower, so line B is likely for bicycle.

Step4: Calculate airplane speed

Speed = $\frac{\text{Distance}}{\text{Time}}$, for airplane at 1 hour it travels 200 miles, so speed is $\frac{200}{1}=200$ miles per hour.

Step5: Calculate automobile speed

Automobile travels 200 miles in 8 hours, speed = $\frac{200}{8}=25$ miles per hour.

Step6: Extend airplane line

Use the slope (200 miles per hour) to extend.

Step7: Calculate airplane distance at 1.5 hours

Distance = speed×time = 200×1.5 = 300 miles.

Step8: Extend automobile line

Use the slope (25 miles per hour) to extend.

Step9: Calculate automobile distance after 3 - more hours

Initial 200 miles + (25×3)=200 + 75 = 275 miles.

Answer:

1. (a) 100, (d) 0.5
2. (c) 200, (d) 8
3. (b) line B
4. 200
5. 25
6. (Graph - cannot be shown in text, but extend the airplane line with the same slope)
7. 300
8. (Graph - cannot be shown in text, but extend the automobile line with the same slope)
9. 275