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

[Pushoam]

Homework Statement

Homework Equations

v_av = 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?

 

[TSny]

Take an arbitrary time t_o. How can you graphically determine the average velocity for the time interval between t = 0 and t = t_o? [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?

 

[cnh1995]

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

Irodov?

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.

 

[Chestermiller]

As TSny indicates, you can pretty much determine the answer for part c by eye, just by looking at the graph.

 

[Pushoam]

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.

Irodov?

Yes

Thanks to all for replying.

 

[TSny]

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.

 

[Pushoam]

Thanks, TSny