Given acceleration graph, determine v vs. t and x vs. t graph?

In summary, the discussion involves a problem with a title involving t=0, x=0 and v=0. The equations used are the kinematic equations and the area of triangle and rectangle. The problem involves a misunderstanding regarding a parabola and a curved line in a graph. The correct solution involves finding the displacement using the equation x=a/2 t^2 and recognizing the curvature of the parabola. The discussion also mentions the importance of measuring directly from graphs rather than guessing.
  • #1
timnswede
101
0

Homework Statement


The title, and assume that t=0, x=0 and v=0.

Homework Equations


Kinematic equations, and area of triangle and rectangle.

The Attempt at a Solution


2o5h9Bo.png

I see what I did wrong with the part that is circled "parabola", as it should be just a straight line, but I am lost as to what is wrong at the part that is circled "curved up". It's speeding up during that part so wouldn't it make sense that the slope is steepest at the top of that section?
 
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  • #2
Instead of guessing, why don't you divide up the time between 10 and 25 secs and on your velocity graph "count squares" for each increment in area as you step through time?

And where you have the velocity steady at 0 m/s for a number of seconds, what will be happening to your displacement over that interval?

There's no excuse for guessing when you can measure directly off the graphs! :cool:
 
  • #3
I think I see what I did wrong, it should go all the way down -375, then a straight line, and then curved down again another 84.375 m right? This was using kinematic equations. So from 10 to 25 seconds it would be curved up, but instead of going towards the positive x it would keep going negative? And when velocity is 0 displacement doesn't change. This is a rough sketch of what it would look like.
pDhEI5E.png
 
  • #4
timnswede said:
I think I see what I did wrong, it should go all the way down -375, then a straight line, and then curved down again another 84.375 m right? This was using kinematic equations. So from 10 to 25 seconds it would be curved up, but instead of going towards the positive x it would keep going negative? And when velocity is 0 displacement doesn't change. This is a rough sketch of what it would look like.
You are right that the displacement is negative all the time, as the velocity is negative.
But think of the equation for displacement, when the initial velocity is zero: x=a/2 t2. It is a parabola, upward open when a >0 and upside down when a<0. Check the curvatures.
 
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Likes timnswede
  • #5
Ah OK, that makes sense. I think I was too caught up with velocity being negative. The way you said I should do it makes it much easier though, thank you.
 
  • #6
Are you going to post another sketch?
 

FAQ: Given acceleration graph, determine v vs. t and x vs. t graph?

How do I determine the velocity vs. time graph from an acceleration graph?

To determine the velocity vs. time graph from an acceleration graph, you can use the integral function to find the area under the acceleration graph. This area represents the change in velocity over a certain time interval. Plotting these values on a graph will give you the velocity vs. time graph.

Can I determine the position vs. time graph from an acceleration graph?

Yes, you can determine the position vs. time graph from an acceleration graph by using the double integral function. This will give you the area under the velocity graph, which represents the change in position over time. Plotting these values on a graph will give you the position vs. time graph.

How does the shape of the acceleration graph affect the velocity vs. time and position vs. time graphs?

The shape of the acceleration graph directly affects the velocity vs. time and position vs. time graphs. The slope of the acceleration graph represents the change in velocity, and the area under the acceleration graph represents the change in position. Therefore, the steeper the slope or larger the area, the greater the change in velocity or position over time.

Can I determine the acceleration from a velocity vs. time graph?

Yes, you can determine the acceleration from a velocity vs. time graph by taking the derivative of the velocity function. The slope of the velocity graph at any given point represents the acceleration at that point.

Is it possible to determine the initial velocity and position from an acceleration graph?

Yes, it is possible to determine the initial velocity and position from an acceleration graph by analyzing the initial conditions and using the appropriate equations. The initial velocity can be found by looking at the y-intercept of the velocity vs. time graph, and the initial position can be found by looking at the y-intercept of the position vs. time graph.

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