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Use the graph showing the motion of a person over time to answer the question.

The vertical axis is labeled, position from home (km), and ranges from a 0 km to 14 km. The horizontal axis is labeled, time (minutes) and labeled from 0 minutes to 50 minutes. The graph shows a line that starts from the origin and slopes upward to 12 km at 10 minutes. The line remains at 12 km from 10 minutes to 30 minutes. The line slopes downward from 12 km to 0 km from 30 minutes to 45 minutes.

Which statement correctly compares his motion during the first 10 minutes to his motion during the last 10 minutes?

(1 point)
Responses

He is speeding up during the first 10 minutes and slowing down during the last 10 minutes.
He is speeding up during the first 10 minutes and slowing down during the last 10 minutes.

He is going faster and in a different direction during the first 10 minutes than in the last 10 minutes.
He is going faster and in a different direction during the first 10 minutes than in the last 10 minutes.

His acceleration increases during the first 10 minutes and decreases during the last 10 minutes.
His acceleration increases during the first 10 minutes and decreases during the last 10 minutes.

He is going slower and in a different direction during the first 10 minutes than in the last 10 minutes.

1 answer

To analyze the motion based on the description of the graph:

  1. First 10 minutes: The person starts from the origin (0 km) and moves upward to 12 km at a steady rate. This indicates positive motion with a constant speed (since the line slopes upward consistently).

  2. Last 10 minutes (from 35 minutes to 45 minutes): The person moves downward from 12 km back to 0 km. This indicates negative motion as they are returning to the starting point, again at a constant rate (given the straight downward slope).

Now, let's look at the responses:

  1. "He is speeding up during the first 10 minutes and slowing down during the last 10 minutes."

    • This is incorrect. He is maintaining a steady speed during both segments.

  2. "He is going faster and in a different direction during the first 10 minutes than in the last 10 minutes."

    • This is incorrect. Speed is constant; the direction changes, but "faster" implies an increase in speed which is not the case.

  3. "His acceleration increases during the first 10 minutes and decreases during the last 10 minutes."

    • This is incorrect. There is no acceleration since he moves at a constant speed in both segments.

  4. "He is going slower and in a different direction during the first 10 minutes than in the last 10 minutes."

    • This is incorrect because he is not going slower, just changing direction but maintaining the same speed.

After evaluating all options, none are true given that he maintains constant speed in both segments. However, if we consider movement direction, options regarding direction might be applicable but don’t correctly address the speed aspect.

The best option to choose, based on the context of direction changes, would technically be the option where there is a recognition of change in direction, even though the speed is constant not slower or faster. But since accuracy matters, none of the given statements are entirely correct.

If one must choose, the statement regarding different directions would be closest, even if inaccurately mentioning speed.

Conclusively: there isn't a correct response based on the speed maintained throughout the graph's movement.