Finding acceleration on a position-time graph

[salmayoussef]

The graph below shows a plot of the position of a particle as a function of time. I need help determining whether the statements concerning the motion of the particle are true or false.

The graph: http://imgur.com/yNeHoF3

? - The instantaneous acceleration at B is zero.
True - The instantaneous velocity at F is zero.
? - The average acceleration over segment AE is less than zero.
False - The average velocity over segment FG is zero.

That's what I have so far! I'm not even sure if the last one is right. I've looked it up, and I can't find how to find acceleration on a position-time graph, only velocity. Any help would be great!

 

[olivermsun]

How do you find velocity on a position time graph?

Acceleration is change of velocity with time.

If you know how to find the velocity, can you determine whether it is changing with time?

 

[happysmiles36]

The graph below shows a plot of the position of a particle as a function of time. I need help determining whether the statements concerning the motion of the particle are true or false.

The graph: http://imgur.com/yNeHoF3

? - The instantaneous acceleration at B is zero.
True - The instantaneous velocity at F is zero.
? - The average acceleration over segment AE is less than zero.
False - The average velocity over segment FG is zero.

That's what I have so far! I'm not even sure if the last one is right. I've looked it up, and I can't find how to find acceleration on a position-time graph, only velocity. Any help would be great!

For x>0
Think of a position time graph as a curved line (exponential)(y=x²)
Now think the velocity time graph which would be a slanted line (y=x)
Now think of the acceleration time graph, which would be a straight horizontal line. <-- (The slope of a velocity time graph gives you the acceleration)

From this we know what the first answer.

For the second statement, when the velocity is 0, the slope of a position time graph is 0, because the slope of a position time graph gives velocity. So what should the position time graph look like?

For the third statement, when the acceleration is less than 0. What does that mean in terms of the velocity? and from this what does that mean in terms of the position? (Hint: Think direction)

 

[salmayoussef]

From this we know what the first answer.

For the second statement, when the velocity is 0, the slope of a position time graph is 0, because the slope of a position time graph gives velocity. So what should the position time graph look like?

For the third statement, when the acceleration is less than 0. What does that mean in terms of the velocity? and from this what does that mean in terms of the position? (Hint: Think direction)

I put the first answer as true.
For the second one, the graph shows that the displacement at F is 0 and to find the velocity of that would mean 0/time which would be 0.
For the third one, if the acc. is less than 0, wouldn't that mean it's slowing down? Or just accelerating in the opposite direction?

 

[olivermsun]

I put the first answer as true.
For the second one, the graph shows that the displacement at F is 0 and to find the velocity of that would mean 0/time which would be 0.

Velocity isn't position over time, it's change in position over time. The position is definitely moving in the negative direction at instant F.

For the third one, if the acc. is less than 0, wouldn't that mean it's slowing down? Or just accelerating in the opposite direction?

The thing starts at A with some initial velocity (hence the graph is initially rising at some slope). Between A and E, does the object go as far as it would have if it had kept that initial velocity?

 

[salmayoussef]

Between A and E, does the object go as far as it would have if it had kept that initial velocity?

No, definitely not. And what would that mean for the acceleration?

 

[olivermsun]

Yowsers, disregard what I said about A to E.

Think about it this way: what's the velocity at A? What's the velocity at E?
What net acceleration had to happen between A and E?