Question
Velocity vs time graph
Time (sec) Displacement (m) Velocity (m/s)
0 0 0
0.5 1.25 5
1 5 10
1.5 11.25 15
Based on the data table, what evidence best suggests that this might be an object in freefall?
Responses
A The velocity of the object is increasing.The velocity of the object is increasing.
B The acceleration of the object is increasing.The acceleration of the object is increasing.
C The change in displacement is increasing at a constant rate.The change in displacement is increasing at a constant rate.
D The acceleration for each interval is a constant of 10 m/s/s.
Time (sec) Displacement (m) Velocity (m/s)
0 0 0
0.5 1.25 5
1 5 10
1.5 11.25 15
Based on the data table, what evidence best suggests that this might be an object in freefall?
Responses
A The velocity of the object is increasing.The velocity of the object is increasing.
B The acceleration of the object is increasing.The acceleration of the object is increasing.
C The change in displacement is increasing at a constant rate.The change in displacement is increasing at a constant rate.
D The acceleration for each interval is a constant of 10 m/s/s.
Answers
GPT-4o mini
To determine if the object could be in free fall based on the provided data, reviewing the velocity values is crucial. In free fall, the velocity of an object increases at a constant rate due to the acceleration of gravity (approximately \(9.81 \, \text{m/s}^2\)).
Let's analyze the options given:
A. **The velocity of the object is increasing.**
- This statement is true based on the velocity data provided (5 m/s at 0.5 sec, 10 m/s at 1 sec, and 15 m/s at 1.5 sec). The velocity increases with time, which is consistent with free fall.
B. **The acceleration of the object is increasing.**
- This statement is not supported by the data. The acceleration should be constant in free fall, not increasing.
C. **The change in displacement is increasing at a constant rate.**
- This is misleading. The displacements are not increasing at a constant rate. The intervals indicate the displacement is increasing at an increasing rate, which suggests acceleration.
D. **The acceleration for each interval is a constant of 10 m/s/s.**
- To check this, we calculate the acceleration between intervals.
- Between 0s and 0.5s: \( a = \frac{(5 \, \text{m/s} - 0 \, \text{m/s})}{0.5 \, \text{s}} = 10 \, \text{m/s}^2 \)
- Between 0.5s and 1s: \( a = \frac{(10 \, \text{m/s} - 5 \, \text{m/s})}{0.5 \, \text{s}} = 10 \, \text{m/s}^2 \)
- Between 1s and 1.5s: \( a = \frac{(15 \, \text{m/s} - 10 \, \text{m/s})}{0.5 \, \text{s}} = 10 \, \text{m/s}^2 \)
The acceleration is constant at \(10 \, \text{m/s}^2\), aligning with the behavior of an object in free fall (disregarding air resistance).
From this analysis, the best evidence to suggest that this might be an object in free fall is:
**D** The acceleration for each interval is a constant of 10 m/s/s.
Let's analyze the options given:
A. **The velocity of the object is increasing.**
- This statement is true based on the velocity data provided (5 m/s at 0.5 sec, 10 m/s at 1 sec, and 15 m/s at 1.5 sec). The velocity increases with time, which is consistent with free fall.
B. **The acceleration of the object is increasing.**
- This statement is not supported by the data. The acceleration should be constant in free fall, not increasing.
C. **The change in displacement is increasing at a constant rate.**
- This is misleading. The displacements are not increasing at a constant rate. The intervals indicate the displacement is increasing at an increasing rate, which suggests acceleration.
D. **The acceleration for each interval is a constant of 10 m/s/s.**
- To check this, we calculate the acceleration between intervals.
- Between 0s and 0.5s: \( a = \frac{(5 \, \text{m/s} - 0 \, \text{m/s})}{0.5 \, \text{s}} = 10 \, \text{m/s}^2 \)
- Between 0.5s and 1s: \( a = \frac{(10 \, \text{m/s} - 5 \, \text{m/s})}{0.5 \, \text{s}} = 10 \, \text{m/s}^2 \)
- Between 1s and 1.5s: \( a = \frac{(15 \, \text{m/s} - 10 \, \text{m/s})}{0.5 \, \text{s}} = 10 \, \text{m/s}^2 \)
The acceleration is constant at \(10 \, \text{m/s}^2\), aligning with the behavior of an object in free fall (disregarding air resistance).
From this analysis, the best evidence to suggest that this might be an object in free fall is:
**D** The acceleration for each interval is a constant of 10 m/s/s.