Graphical analysis, vx, ax, and xf problems

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In summary: The area under the first section (0-2 seconds) would be 2 seconds times 20 m/s, which is 40 meters. The area under the second section (2-4 seconds) would be 4 seconds times 20 m/s, which is also 40 meters. The area under the third section (4-6 seconds) would be 2 seconds times -20 m/s, which is -40 meters. The area under the fourth section (6-8 seconds) would be 2 seconds times -40 m/s, which is -80 meters. Adding all these areas together gives a total displacement of -40 meters. So in summary, the displacement from 0 to 8 seconds is -40 meters.For
  • #1
mark9159
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1.) A car travels at 15 m/s for 10s. It then speeds up with a constant acceleration of 2.00 m/s^2 for 15s. At the end of this time, what is its velocity?

My answer: Vxf= 45 m/s

2.) An object is moving in a straight line with constant acceleration. Initially it is traveling at 16 m/s. Three seconds later it is traveling at 10 m/s. How far does it move during this time?

My answer: 39m

3.) A ball is thrown downward from the top of a building with an initial speed of 25 m/s. It strikes the ground after 2.0s. How high is the building?

My answer: 30m

4.) I can't draw a graph on here, so I'll describe it to the best of my abilities. It is a velocity versus(m/s) vs. time (s) graph.

The graph starts at the origin. At 2.0s, velocity increases 20 m/s. From 2.0 to 4.0 seconds, velocity is constant at 20m/s. From 4.0 to 6.0s, velocity is decreasing by 20 m/s. At 6.0 to 8.0s, velocity is decreasing another 20 m/s.

question: What is the displacement from 0 to 8.0s?

My answer: Honestly, I didn't know how to approach this one. All i did was I added up and subtracted...and got 20m.

5.) Which student used the least precise scale?
A. 49.06
B. 49
C. 50
D. 49.2
 
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  • #2
mark9159 said:
1.) A car travels at 15 m/s for 10s. It then speeds up with a constant acceleration of 2.00 m/s^2 for 15s. At the end of this time, what is its velocity?

My answer: Vxf= 45 m/s

2.) An object is moving in a straight line with constant acceleration. Initially it is traveling at 16 m/s. Three seconds later it is traveling at 10 m/s. How far does it move during this time?

My answer: 39m

3.) A ball is thrown downward from the top of a building with an initial speed of 25 m/s. It strikes the ground after 2.0s. How high is the building?

My answer: 30m

4.) I can't draw a graph on here, so I'll describe it to the best of my abilities. It is a velocity versus(m/s) vs. time (s) graph.

The graph starts at the origin. At 2.0s, velocity increases 20 m/s. From 2.0 to 4.0 seconds, velocity is constant at 20m/s. From 4.0 to 6.0s, velocity is decreasing by 20 m/s. At 6.0 to 8.0s, velocity is decreasing another 20 m/s.

question: What is the displacement from 0 to 8.0s?

My answer: Honestly, I didn't know how to approach this one. All i did was I added up and subtracted...and got 20m.

5.) Which student used the least precise scale?
A. 49.06
B. 49
C. 50
D. 49.2

For question 4. Since displacement is the integral of velocity, you should calculate the area under the velocity curve, from 0 to 8 secods.
 
  • #3


My answer: B. 49

Explanation: The least precise scale is the one with the fewest number of digits after the decimal point. In this case, option B has no digits after the decimal point, making it the least precise.
 

FAQ: Graphical analysis, vx, ax, and xf problems

1. What is graphical analysis and why is it important?

Graphical analysis is a method used to visually represent and analyze data in the form of graphs. It is important because it allows scientists to easily identify patterns, trends, and relationships in the data, which can then be used to draw conclusions and make predictions.

2. What is vx and how is it different from ax?

Vx, also known as velocity in the x direction, is a measure of an object's speed and direction in a specific direction. It is different from ax, which stands for acceleration in the x direction, as acceleration measures the rate of change of an object's velocity. In other words, vx is a measure of an object's movement, while ax is a measure of the change in that movement.

3. How can I solve xf problems using graphical analysis?

To solve xf problems using graphical analysis, you can plot the data points on a graph and use the slope of the line to calculate the object's displacement (xf) over a given time interval. The slope of the line represents the object's velocity, and the area under the line represents the object's displacement.

4. What are some common mistakes to avoid when analyzing graphs for vx, ax, and xf problems?

One common mistake is misinterpreting the slope of a line on a graph. The slope represents the rate of change, not the actual value of vx or ax. Another mistake is not paying attention to the units on the axes of the graph, as this can lead to incorrect calculations. Additionally, it is important to make sure the data points are accurate and precise, as they can greatly affect the analysis.

5. How can graphical analysis help in predicting future behavior of an object?

Graphical analysis can help in predicting future behavior of an object by identifying patterns and trends in the data. By analyzing the shape and direction of the graph, scientists can make predictions about how an object's velocity, acceleration, and displacement will change in the future. This can be useful in many fields, such as predicting weather patterns or the trajectory of a spacecraft.

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