Kinematics 4 -- Calculate the velocity from the position versus time graph

In summary, the conversation discusses a problem in determining average velocity and the use of numerical methods to solve it. It also mentions the interpretation of average velocity as the slope of a line and finding the time moment when the line passes through the origin. The solution is found to be at 16 seconds.
  • #1
Pushoam
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Homework Statement


upload_2017-7-11_21-51-59.png


Homework Equations


vav = total distance traveled/ total time taken

The Attempt at a Solution


I have a problem in part c .
How am I supposed to solve it?
Is there any standard way to solve it?
 

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  • #2
Take an arbitrary time to. How can you graphically determine the average velocity for the time interval between t = 0 and t = to? [Edit: Can you interpret the average velocity as the slope of some line?]

It might help to first take a specific example. Suppose you take t0 = 10 s. How would you get the average velocity for the time interval t = 0 to t = 10 s? Does this average velocity equal the instantaneous velocity at t = 10 s?
 
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  • #3
Pushoam said:
I have a problem in part c .
How am I supposed to solve it?
Is there any standard way to solve it?
Irodov?

Pushoam said:
Is there any standard way to solve it?
One standard way could be using numerical methods. Newton's forward interpolation or Lagrange's interpolation will work.
You can find the displacement-time relationship for three intervals: i)from t=0 to t=10s ii)from t=10 to t=14.5s iii) from t=14.5 to t=20s.
Once you have the s-t relationship, you can find t0.
 
  • #4
As TSny indicates, you can pretty much determine the answer for part c by eye, just by looking at the graph.
 
  • #5
TSny said:
Edit: Can you interpret the average velocity as the slope of some line?]
Thanks.
I got it.
I never interpreted average velocity as the slope of some line. Thanks for this insight.
So, what I have to find out is the time moment at which the line whose slope defines the instantaneous velocity passes through the origin. This time moment turns out to be 16 s.
cnh1995 said:
Irodov?

Yes

Thanks to all for replying.
 
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  • #6
Pushoam said:
So, what I have to find out is the time moment at which the line whose slope defines the instantaneous velocity passes through the origin. This time moment turns out to be 16 s.
Yes. Good work.
 
  • #7
Thanks, TSny
 

1. How do you calculate velocity from a position versus time graph?

To calculate velocity from a position versus time graph, you will need to find the slope of the line on the graph. This can be done by selecting two points on the line and then using the slope formula (change in position/change in time) to determine the velocity at that point.

2. Can you determine the direction of velocity from a position versus time graph?

Yes, the direction of velocity can be determined by the slope of the line on the graph. If the slope is positive, the object is moving in a positive direction, and if the slope is negative, the object is moving in a negative direction. Additionally, the shape of the line can also indicate the direction of velocity. A straight line indicates constant velocity, while a curved line indicates changing velocity.

3. What is the difference between average velocity and instantaneous velocity?

Average velocity is the overall rate of change in position over a given time interval, while instantaneous velocity is the rate of change in position at a specific moment in time. Average velocity is calculated by dividing the total change in position by the total change in time, while instantaneous velocity is calculated by finding the slope of the line tangent to the position versus time graph at a specific point.

4. Can you calculate acceleration from a position versus time graph?

Yes, you can calculate acceleration from a position versus time graph by finding the slope of the velocity versus time graph. Acceleration is the rate of change in velocity over time, so the slope of the velocity versus time graph will give you the acceleration at that point.

5. How can you use a position versus time graph to determine the distance traveled by an object?

You can determine the distance traveled by an object from a position versus time graph by calculating the area under the curve. This can be done by breaking the graph into smaller sections, finding the area of each section (base x height), and then summing up all the areas to get the total distance traveled. Alternatively, you can also use the displacement formula (final position - initial position) to find the total distance traveled.

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