Question

1. the graph shows the position of an object over time.

based on the graph, which of these scenarios best describes the motion of the object?

the object moves forward for 4 seconds, stops for 2 seconds, then moves backward at a constant speed until it reaches its starting point

the object moves forward for 6 seconds, stops for 2 seconds, then moves backward, gradually slowing down until it reaches its starting point

the object moves forward for 6 seconds, stops for 4 seconds, then gradually moves backward to its starting point.

the object moves forward for 4 seconds, stops for 2 seconds, then moves backward, first slowly and then at a faster pace, until it reaches its starting point.

Explanation:

1. Analyze the forward motion: The position increases from \( t = 0 \) to \( t = 4 \) seconds (so forward for 4 seconds).
2. Analyze the stopping phase: From \( t = 4 \) to \( t = 6 \) seconds, the position is constant (so stops for \( 6 - 4=2 \) seconds).
3. Analyze the backward motion:

• From \( t = 6 \) to \( t = 10 \) seconds, the graph is a curve (decreasing position, slow rate of decrease as it's a curve).
• From \( t = 10 \) to \( t = 12 \) seconds, the graph is a straight line (decreasing position, faster rate of decrease as it's a steeper straight line).
• Finally, it reaches the starting point (\( \text{position} = 0 \)) at \( t = 12 \) seconds.

This matches the description: "The object moves forward for 4 seconds, stops for 2 seconds, then moves backward, first slowly and then at a faster pace, until it reaches its starting point."

Answer:

The object moves forward for 4 seconds, stops for 2 seconds, then moves backward, first slowly and then at a faster pace, until it reaches its starting point. (the last option)