Find Velocitiy from an Acceleration vs. Displacement Graph

In summary, the conversation discusses using the graph of the a-s relationship for a rocket moving along a straight horizontal track to determine its velocity at different points along the track. The integral of ads is used to calculate the velocity, and it is equal to the integral of vdv. By setting the two equations equal to each other, the velocity at S2 = 70m is found to be 40 m/s.
  • #1
CGI
74
1

Homework Statement


The a-s graph for a rocket moving along a straight horizontal track has been experimentally determined. If the rocket starts from rest, determine its speed at the instants s = 20m, 50m, and 70m, respectively. On the graph, S1 = 50m, a1 = 10 m/s^2, S2 = 70m, and a2 = 20 m/s^2

Homework Equations


ads = vdv [/B]

The Attempt at a Solution


I know that the solution for the velocity at S2 = 70m is V = 40 m/s, but I'm not sure how to get there.
I know we talked about the relationship for ads = vdv so I tried taking the integral on both sides to calculate for the velocity.

I tried to solve for the velocity at S2

The integral from 0 to v of vdv = the integral from 0 to 20 of ads
So, V^2/2 = 20s which means V^2 = 40s where S = 70 meters.
So I get V = √(40)(70) = 52.9, which is not correct.

20160116_194713.jpg
Any help would be much appreciated!
 
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  • #2
CGI said:
The integral from 0 to v of vdv = the integral from 0 to 20 of ads

What is the graphical way to interpret the integral of ads from s = 0 to s = 70 m?
 
  • #3
My best guess is the area of that section from 0 to 70? Is that in the right direction?
 
  • #4
CGI said:
My best guess is the area of that section from 0 to 70? Is that in the right direction?
Yes.
 
  • #5
Okay, so I got 800 for the total area underneath, but I'm not sure what the next step is
 
  • #6
CGI said:
Okay, so I got 800 for the total area underneath, but I'm not sure what the next step is

Good.

How is the integral of ads related to the integral of vdv?
 
  • #7
They're equal to each other? So I could set v^2/2 = 800 which in the end makes v = 40.

Did I think about that correctly?
 
  • #8
CGI said:
They're equal to each other? So I could set v^2/2 = 800 which in the end makes v = 40.

Did I think about that correctly?
Yes.
 

1. What is the formula for finding velocity from an acceleration vs. displacement graph?

The formula for finding velocity from an acceleration vs. displacement graph is v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

2. How do you interpret an acceleration vs. displacement graph?

An acceleration vs. displacement graph shows the relationship between acceleration and displacement over time. The slope of the graph represents the acceleration, while the area under the graph represents the displacement.

3. Can you find the velocity at a specific point on the graph?

Yes, you can find the velocity at a specific point on the graph by finding the slope of the tangent line at that point. The slope of the tangent line represents the instantaneous velocity at that point.

4. What units are used for velocity, acceleration, and displacement on the graph?

Velocity is typically measured in meters per second (m/s), acceleration in meters per second squared (m/s²), and displacement in meters (m).

5. How does the shape of the graph affect the velocity calculation?

The shape of the graph can affect the velocity calculation in different ways. For example, a constant positive slope would indicate a constant acceleration, while a curved slope would indicate a changing acceleration. The velocity can also be calculated by finding the area under the graph, which would be affected by the shape of the graph.

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