To analyze the problem, we first need to determine the durations of segments 2 and 3 based on the provided velocity versus time graph details:
- Segment 1: From 0 seconds to 60 seconds (Δt = 60 seconds) with a velocity change from 0 m/s to 8 m/s.
- Segment 2: From 60 seconds to 150 seconds (Δt = 90 seconds) with a velocity change from 8 m/s to 14 m/s.
- Segment 3: From 150 seconds to 240 seconds (Δt = 90 seconds) with a velocity change from 14 m/s to 29 m/s.
Now that we have identified that:
- Segment 2 spans 90 seconds.
- Segment 3 also spans 90 seconds.
Since both segments 2 and 3 have equal durations in time (90 seconds), we can now look at the change in velocity in each segment to understand the forces involved.
The force acting on an object is related to acceleration, which can be derived from the change in velocity over the change in time.
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Acceleration for Segment 2: \[ a_2 = \frac{\Delta v}{\Delta t} = \frac{14, \text{m/s} - 8, \text{m/s}}{90, \text{s}} = \frac{6, \text{m/s}}{90, \text{s}} = \frac{1}{15}, \text{m/s}^2 \]
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Acceleration for Segment 3: \[ a_3 = \frac{\Delta v}{\Delta t} = \frac{29, \text{m/s} - 14, \text{m/s}}{90, \text{s}} = \frac{15, \text{m/s}}{90, \text{s}} = \frac{1}{6}, \text{m/s}^2 \]
As a result, the forces acting during segments 2 and 3 differ since the accelerations differ. This means the statement we are looking for must indicate that the periods of time are equal but the forces acting in each segment are different.
Based on this analysis, the correct response is:
Segments 2 and 3 have equal periods of time but the force during segment 2 is different than the force during segment 3.
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