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The diagram shows the position of a race car at different times as the car drives along a straight road.



A diagram.Short description, A diagram.,Long description,
A diagram shows time and position.

Zero seconds, zero meters.
Two seconds, 100 meters.
Four seconds, 200 meters.
Six seconds, 300 meters.
Eight seconds, 400 meters.
Ten seconds, 500 meters.
Twelve seconds, 600 meters.
Fourteen seconds, 700 meters.

Question
Which graph shows the speed of the race car versus time?

Answer options with 4 options
A.
A line graph.Short description, A line graph.,Long description,
A line graph shows the x-axis is labeled Time in seconds from 0 to 14, and the y-axis is labeled Speed in meters per second from 0 to 800. The line begins at 0 seconds; 0 meters per second and increases steadily, ending at 14 seconds; 700 meters per second.

C.
A line graph.Short description, A line graph.,Long description,
A line graph shows the x-axis is labeled Time in seconds from 0 to 14, and the y-axis is labeled Speed in meters per second from 0 to 80. The line begins at 0 seconds; 0 meters per second and increases steadily, ending at 14 seconds; 70 meters per second.

B.
A line graph.Short description, A line graph.,Long description,
A line graph shows the x-axis is labeled Time in seconds from 0 to 14, and the y-axis is labeled Speed in meters per second from 0 to 60. The line begins at 0 seconds; 50 meters per second and remains flat and steady, ending at 14 seconds; 50 meters per second.

D.
A line graph.Short description, A line graph.,Long description,
A line graph shows the x-axis is labeled Time in seconds from 0 to 14, and the y-axis is labeled Speed in meters per second from 0 to 60. The line begins at 0 seconds; 50 meters per second and decreases steadily, ending at 14 seconds; 15 meters per second.

1 answer

To determine which graph accurately reflects the speed of the race car versus time, we first need to find the speed of the car over the given time intervals based on the position data.

  1. Calculate the speed of the race car:

The position of the race car at different times is provided as follows:

  • At 0 seconds: 0 meters
  • At 2 seconds: 100 meters
  • At 4 seconds: 200 meters
  • At 6 seconds: 300 meters
  • At 8 seconds: 400 meters
  • At 10 seconds: 500 meters
  • At 12 seconds: 600 meters
  • At 14 seconds: 700 meters

The speed can be calculated using the formula: \[ \text{Speed} = \frac{\text{Change in Position}}{\text{Change in Time}} \]

The changes in position for each 2-second interval are:

  • From 0 to 2 seconds: \( \frac{100 - 0}{2 - 0} = 50 \) meters/second
  • From 2 to 4 seconds: \( \frac{200 - 100}{4 - 2} = 50 \) meters/second
  • From 4 to 6 seconds: \( \frac{300 - 200}{6 - 4} = 50 \) meters/second
  • From 6 to 8 seconds: \( \frac{400 - 300}{8 - 6} = 50 \) meters/second
  • From 8 to 10 seconds: \( \frac{500 - 400}{10 - 8} = 50 \) meters/second
  • From 10 to 12 seconds: \( \frac{600 - 500}{12 - 10} = 50 \) meters/second
  • From 12 to 14 seconds: \( \frac{700 - 600}{14 - 12} = 50 \) meters/second

As we can see, the speed of the race car is constant at 50 meters per second for the entire duration from 0 to 14 seconds.

  1. Determine the correct graph:

Now, let's analyze the answer choices based on our findings:

  • Option A shows a speed increasing to 700 meters per second, which is incorrect.
  • Option B shows a constant speed of 50 meters per second, which matches our calculations, but it begins at 50 meters per second rather than at 0, which is incorrect.
  • Option C shows a speed increasing to 70 meters per second, which is incorrect.
  • Option D shows a speed starting at 50 meters per second and decreasing, which is also incorrect.

None of the options provided correctly reflects that the speed should start at 50 meters per second and remain constant throughout the time interval. However, Option B is the closest option, as it reflects the constant speed, but it inaccurately starts at 50 meters per second instead of correctly starting at 0 m/s.

In conclusion, if we had to choose the best option among the listed ones, the answer would be Option B, despite its initial inaccuracy in starting value.