Find distance traveled using acceleration graph

So the correct distance traveled in the first 20 seconds is 150 m.In summary, the question asks to find the distance traveled in the first 20 seconds using a given graph. The attempt at a solution involved using the formula a = [2(x-x(sub-i))] / 2, but this was incorrect. After some attempts, the correct answer was found to be 150 m, taking into account the distance traveled with uniform velocity during 10 to 15 seconds.
  • #1
denxnis
6
0

Homework Statement


Here is a link to the graph.

http://www.webassign.net/pse/pse6_p2-12.gif

Find the distance traveled in the first 20 seconds.


Homework Equations



Integral once = velocity
Integral twice = position

I attempted to use the following formula:

a = [ 2 ( x - x(sub-i) ) ] / 2

The Attempt at a Solution



When I integrated twice i came up with, 100m however this is incorrect
Then I somehow came up with 137.5, this is incorrect.
I attempted to use the following formula:

a = [ 2 ( x - x(sub-i) ) ] / 2

unfortunately I came up empty handed.

Please help! this problem is killing me.
Thank you for your time.
 
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  • #2
While coming up with 137.5 m, I think, you have left out the distance traveled with uniform velocity during 10 to 15 seconds.
 
  • #3


I would first like to clarify that acceleration is the rate of change of velocity, not the rate of change of position. Therefore, the formula you attempted to use is not appropriate for finding distance traveled.

To find distance traveled using an acceleration graph, you can use the area under the curve. In this case, the graph represents constant acceleration, so the area under the curve can be calculated using the formula: distance = initial velocity * time + 0.5 * acceleration * time^2.

In the first 20 seconds, the initial velocity is 0 m/s and the acceleration is 2 m/s^2. Therefore, the distance traveled in the first 20 seconds would be:

distance = 0 * 20 + 0.5 * 2 * (20)^2 = 0 + 0.5 * 2 * 400 = 400 m

So the distance traveled in the first 20 seconds is 400 meters. It is important to note that this formula only works for constant acceleration, so it may not be appropriate for more complex acceleration graphs. In those cases, you may need to use calculus to find the distance traveled. I hope this helps with your problem.
 

1. How do you find distance traveled using an acceleration graph?

To find distance traveled using an acceleration graph, you must first calculate the area under the curve of the graph. This area represents the displacement, or distance traveled, during the given time period. You can use the formula distance = (1/2) x acceleration x time2 to calculate the area and find the distance traveled.

2. Can you use any acceleration graph to find distance traveled?

Yes, as long as the graph shows the acceleration over time, you can use it to find the distance traveled. It is important to ensure that the units of the graph are consistent, such as using meters per second squared for acceleration and seconds for time.

3. How does the shape of the acceleration graph affect the distance traveled?

The shape of the acceleration graph can affect the distance traveled because it represents the rate at which the object is accelerating. A steeper curve indicates a higher acceleration, meaning the object is covering more distance in a shorter amount of time. A flatter curve indicates a lower acceleration, meaning the object is covering less distance in the same amount of time.

4. What if the acceleration graph is not a straight line?

If the acceleration graph is not a straight line, you can still use the same method of calculating the area under the curve to find the distance traveled. However, you may need to break the graph into smaller sections and calculate the area for each section separately, then add them together to find the total distance traveled.

5. Can you use an acceleration graph to find the total distance traveled at any point in time?

No, an acceleration graph only shows the acceleration over time and cannot be used to find the total distance traveled at any given point. It can only be used to find the total distance traveled during a specific time period. To find the total distance traveled at a specific point in time, you would need to use a position vs. time graph or the equation distance = initial velocity x time + (1/2) x acceleration x time2.

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