Displacement from an Acceleration Time Graph

In summary, the conversation discusses finding displacement in a kinematics problem. The problem involves determining the position of a moving object at different times and velocities. The student has already solved for the time at which the velocity returns to 54km/h, but is now trying to find the position. They consider using a v-t graph and finding the area under the curve, but are unsure of its accuracy. They also try using the equations xo = vot + 1/2at2 and x = xo + vt, but get incorrect answers. The suggested solution is to set up a(t) functions for the two regions and integrate them twice with respect to time. The student is asked to show their attempts in detail.
  • #1
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Homework Statement


upload_2016-2-5_1-42-37.png

Homework Equations


Kinematic equations
t = 18s when the velocity is back to 54km/h or 15m/s
at t = 2, V = 13.3 m/s
at t = 4.5, velocity is 1.5 m/s
at t = 1, V = 15m/s

The Attempt at a Solution


I have solved the first part and I have the time at which it is 54km/h again, but now I'm trying to figure out
the position. I think I could make a v-t graph and find the area under that curve, but it seems like that would be too hard to accurately represent the graph. Is there any other way to find displacement? I've tried
xo = vot + 1/2at2 but that doesn't seem to help
I also tried
x = xo + vt, but I get 270m as an answer. The correct answer is 178.8, but I just want to understand how to do it. Any help would be much appreciated!
 

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  • #2
What you can try is set up a(t) functions for the two regions and integrate the functions twice wrt time.
 
  • #3
You'll have to show your attempt(s) in detail.
 

1. How is displacement calculated from an acceleration time graph?

The displacement from an acceleration time graph can be calculated by finding the area under the curve. This can be done by dividing the graph into smaller shapes, such as rectangles or triangles, and finding the area of each shape. Then, add up the areas of all the shapes to get the total displacement.

2. What does the slope of an acceleration time graph represent?

The slope of an acceleration time graph represents the acceleration of an object. This is because acceleration is defined as the change in velocity over a certain time period, and the slope of a graph is the change in the y-axis (acceleration) over the change in the x-axis (time).

3. Can displacement be negative on an acceleration time graph?

Yes, displacement can be negative on an acceleration time graph. This occurs when the object is moving in the negative direction, such as when it is slowing down or moving in the opposite direction of the initial motion.

4. How does a constant acceleration affect the displacement on a time graph?

A constant acceleration will result in a straight line on an acceleration time graph. The displacement can then be calculated by finding the area of the triangle formed by the line and the x-axis.

5. What is the difference between displacement and distance on an acceleration time graph?

Displacement and distance are often used interchangeably, but they have different meanings in physics. Displacement refers to the overall change in position of an object, while distance refers to the total length traveled by the object. On an acceleration time graph, displacement is represented by the area under the curve, while distance is represented by the length of the curve itself.

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