Question

Question

Use the image to answer the question.

An illustration shows quadrant one of a coordinate plane where the x-axis and y-axis range from 0 to 6 in increments of 1. The y-axis is titled distance in feet and the x-axis is titled time in seconds. A solid line, labeled A, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 3 comma 6 right parenthesis. A dotted line, labeled B, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 6 right parenthesis. A dashed line, labeled C, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 3 right parenthesis.

Which of these objects would reach 100 feet in the least amount of time?

(1 point)
Responses

object B
object B

object A
object A

They would all reach 100 feet at the same time.
They would all reach 100 feet at the same time.

object C
object C
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Answer 1

To determine which object reaches 100 feet in the least amount of time, we need to analyze the lines on the graph, which represent the relationships between time (x-axis) and distance (y-axis).

1. Object A passes through the points (0,0) and (3,6). The slope (rate of distance per time) can be calculated as follows:

   • Slope = (6 - 0) / (3 - 0) = 6/3 = 2 feet per second.
   • This means it covers 2 feet in 1 second.

2. Object B passes through the points (0,0) and (6,6). The slope is:

   • Slope = (6 - 0) / (6 - 0) = 6/6 = 1 foot per second.
   • This means it covers 1 foot in 1 second.

3. Object C passes through the points (0,0) and (6,3). The slope is:

   • Slope = (3 - 0) / (6 - 0) = 3/6 = 0.5 feet per second.
   • This means it covers 0.5 feet in 1 second.

To find out how long each object takes to reach 100 feet:

• Object A:

  • Time = Distance / Speed = 100 feet / 2 feet per second = 50 seconds.

• Object B:

  • Time = Distance / Speed = 100 feet / 1 foot per second = 100 seconds.

• Object C:

  • Time = Distance / Speed = 100 feet / 0.5 feet per second = 200 seconds.

Conclusion

Object A would reach 100 feet in the least amount of time, taking 50 seconds. Thus, the answer is:

object A