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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

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

object C
object C

object B
object B

object A

1 answer

To determine which object reaches 100 feet in the least amount of time, we need to analyze the velocity represented by each line on the graph.

  1. Object A (solid line) passes through the points (0, 0) and (3, 6). This means in 3 seconds, it reaches 6 feet. The slope (velocity) of this line is calculated as: \[ \text{Slope of A} = \frac{\Delta y}{\Delta x} = \frac{6 - 0}{3 - 0} = \frac{6}{3} = 2 \text{ feet per second.} \]

  2. Object B (dotted line) passes through (0, 0) and (6, 6). So in 6 seconds, it reaches 6 feet. The slope (velocity) of this line is: \[ \text{Slope of B} = \frac{6 - 0}{6 - 0} = \frac{6}{6} = 1 \text{ foot per second.} \]

  3. Object C (dashed line) passes through (0, 0) and (6, 3). This means in 6 seconds, it reaches 3 feet. The slope (velocity) of this line is: \[ \text{Slope of C} = \frac{3 - 0}{6 - 0} = \frac{3}{6} = 0.5 \text{ feet per second.} \]

Now, we will calculate the time each object takes to reach 100 feet.

  • Object A: The time to reach 100 feet can be calculated using the formula: \[ \text{Time} = \frac{\text{Distance}}{\text{Velocity}} = \frac{100}{2} = 50 \text{ seconds.} \]

  • Object B: The same formula gives us: \[ \text{Time} = \frac{100}{1} = 100 \text{ seconds.} \]

  • Object C: For object C: \[ \text{Time} = \frac{100}{0.5} = 200 \text{ seconds.} \]

Based on these calculations, object A reaches 100 feet in 50 seconds, which is the least amount of time.

Therefore, the correct answer is:

object A.