Which of the following statements is true? A) At t = 4 s, object B catches up to object A. B) Over the first 4 s, object B has an average velocity of 5 m/s. C) At t = 4 s, both obj... Which of the following statements is true? A) At t = 4 s, object B catches up to object A. B) Over the first 4 s, object B has an average velocity of 5 m/s. C) At t = 4 s, both objects have covered the same distance. D) Object A is motionless. E) Object B is moving with constant, positive velocity.
Understand the Problem
The question is asking us to analyze a velocity-time graph to determine which of the provided statements about the motion of two objects, A and B, is true.
Answer
None of the statements are true.
Answer for screen readers
None of the statements are true based on the information from the graph.
Steps to Solve
- Analyze the velocities of objects A and B at t = 4 s
From the graph, we see that at $t = 4 \text{ s}$, the velocity of object A is $10 \text{ m/s}$, and the velocity of object B is at $15 \text{ m/s}$. This indicates that object B is moving faster than object A at this point.
- Calculate average velocity of object B
To find the average velocity of object B over the first 4 seconds, we note that the velocity increases linearly from $0 \text{ m/s}$ at $t = 0 \text{ s}$ to $15 \text{ m/s}$ at $t = 4 \text{ s}$. The average velocity ($v_{avg}$) can be calculated as:
$$ v_{avg} = \frac{(0 + 15)}{2} = 7.5 \text{ m/s} $$
- Determine distance covered by both objects at t = 4 s
Distance ($d$) can be calculated using the formula:
$$ d = v_{avg} \times t $$
For object A:
- Average velocity = $5 \text{ m/s}$ (from 0 to 4 seconds)
- Distance = $5 \text{ m/s} \times 4 \text{ s} = 20 \text{ m}$
For object B:
- Average velocity = $7.5 \text{ m/s}$
- Distance = $7.5 \text{ m/s} \times 4 \text{ s} = 30 \text{ m}$
- Evaluate the statements
- Statement A: False, as at t=4s, B is ahead of A.
- Statement B: False; average velocity is $7.5 \text{ m/s}$, not $5 \text{ m/s}$.
- Statement C: False; distances are different (20 m vs 30 m).
- Statement D: False; object A is moving with a velocity of $10 \text{ m/s}$.
- Statement E: False; the velocity of objects is changing over time.
- Identify the correct statement
After evaluating each statement, we find that none of the statements are true regarding the motion of objects A and B.
None of the statements are true based on the information from the graph.
More Information
The velocity-time graph shows how the velocities of the two objects change over time. It's essential to analyze both the velocities and distances to draw accurate conclusions about their motions.
Tips
- Misinterpreting average velocity: Remember that the average velocity calculation must use the correct initial and final velocities over the time interval.
- Failing to compare distances correctly: Always calculate the distance covered by each object before concluding that they are the same.
