Velocity and Acceleration Quick Check
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Question
Use this graph of velocity vs. time for two objects to answer the question.
A velocity versus time graph shows two lines sloping upward from the origin. The line with the higher slope is labeled, C, and the line with smaller slope is labeled, D.
Which statement makes an accurate comparison of the motions for objects C and D?
(1 point)
Responses
Objects C and D have different accelerations but the same velocity throughout the motion.
Objects C and D have different accelerations but the same velocity throughout the motion.
Object D has an acceleration that is greater than the acceleration for C.
Object D has an acceleration that is greater than the acceleration for C.
Object C has an acceleration that is greater than the acceleration for D.
Object C has an acceleration that is greater than the acceleration for D.
Objects C and D have different velocities but the same acceleration.
Objects C and D have different accelerations but the same velocity throughout the motion.
The correct statement that makes an accurate comparison of the motions for objects C and D is:
Object C has an acceleration that is greater than the acceleration for D.
To answer this question, you need to analyze the velocity vs. time graph for objects C and D.
First, let's understand how to interpret a velocity vs. time graph. The slope of a velocity vs. time graph represents the acceleration of an object. A steeper slope indicates a greater acceleration.
Looking at the graph, we can see that line C has a higher slope than line D. This means that object C has a greater acceleration than object D.
Now, let's consider the statement options:
1. Objects C and D have different accelerations but the same velocity throughout the motion.
Since C and D have different slopes, indicating different accelerations, this statement is incorrect.
2. Object D has an acceleration that is greater than the acceleration for C.
This statement is incorrect because the graph shows that object C has a steeper slope, indicating a greater acceleration than object D.
3. Object C has an acceleration that is greater than the acceleration for D.
This statement is correct because the graph shows that line C has a steeper slope, indicating a greater acceleration for object C compared to object D.
4. Objects C and D have different velocities but the same acceleration.
The graph does not provide information about the velocities of objects C and D, so we cannot determine if they have different velocities based on the graph alone. However, we can conclude that they have different accelerations based on the slopes of the lines.
Therefore, the correct statement is: Object C has an acceleration that is greater than the acceleration for D.