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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

object C
object C

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

object A
object A

object B

3 answers

To determine which object would reach 100 feet in the least amount of time, we need to analyze the slopes (rates of distance per time) of the lines A, B, and C:

  1. Line A: It passes through the points (0, 0) and (3, 6). The slope is calculated as follows: \[ \text{slope}_A = \frac{6 - 0}{3 - 0} = \frac{6}{3} = 2 \text{ feet/second} \]

  2. Line B: It passes through the points (0, 0) and (6, 6): \[ \text{slope}_B = \frac{6 - 0}{6 - 0} = \frac{6}{6} = 1 \text{ foot/second} \]

  3. Line C: It passes through the points (0, 0) and (6, 3): \[ \text{slope}_C = \frac{3 - 0}{6 - 0} = \frac{3}{6} = 0.5 \text{ feet/second} \]

Now, we can calculate the time it takes for each object to reach 100 feet using the formula: \[ \text{time} = \frac{\text{distance}}{\text{rate}} \]

  • For Object A: \[ \text{time}_A = \frac{100}{2} = 50 \text{ seconds} \]

  • For Object B: \[ \text{time}_B = \frac{100}{1} = 100 \text{ seconds} \]

  • For Object C: \[ \text{time}_C = \frac{100}{0.5} = 200 \text{ seconds} \]

Based on these calculations, Object A would reach 100 feet in the least amount of time, which is 50 seconds.

Therefore, the answer is:

object A

object a?

Yes, that is correct. Object A would reach 100 feet in the least amount of time.

To summarize the calculations:

  • Object A (slope of 2 feet/second): Reaches 100 feet in 50 seconds.
  • Object B (slope of 1 foot/second): Reaches 100 feet in 100 seconds.
  • Object C (slope of 0.5 feet/second): Reaches 100 feet in 200 seconds.

Thus, among the three objects, object A reaches 100 feet the fastest.