Simple question about Motion graphs/trajectory

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In summary, the velocity of a ball thrown up and reaching the height of its trajectory is equal to zero only for an instant. The acceleration of the ball can be calculated using the slope of the velocity graph, which is constant throughout the motion despite the ball rising and falling. This is due to the unbroken line on the graph, representing the constant acceleration of gravity.
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Two questions:

1.) When you throw a ball up and it reaches the height of its trajectory, is the velocity equal to zero only for an INSTANT or for LESS THAN A SECOND BUT MORE THAN AN INSTANT? The velocity graph is sloping straight downwards with no breaks.

2.) If you are given a x(t) graph that shows a simple parabolic motion (throw ball up and comes down) and a v(t) graph that is a straight line sloping downwards (starting above the x-axis and ending below the x axis), how would you calculate the acceleration (ball is thrown on another planet)?

Any help is appreciated. Thanks.
 
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  • #2
Welcome to PF!

Hi physics213! Welcome to PF! :smile:
physics213 said:
1.) When you throw a ball up and it reaches the height of its trajectory, is the velocity equal to zero only for an INSTANT or for LESS THAN A SECOND BUT MORE THAN AN INSTANT? The velocity graph is sloping straight downwards with no breaks.

Only an instant (in other words, no time at all). :smile:

(Obviously, that's for a ball going straight up. If it's a parabola, then the vertical component is zero for an instant.)
2.) If you are given a x(t) graph that shows a simple parabolic motion (throw ball up and comes down) and a v(t) graph that is a straight line sloping downwards (starting above the x-axis and ending below the x axis), how would you calculate the acceleration (ball is thrown on another planet)?

Hint: what is the definition of acceleration? :smile:
 
  • #3
tiny-tim said:
Hi physics213! Welcome to PF! :smile:


Only an instant (in other words, no time at all). :smile:

(Obviously, that's for a ball going straight up. If it's a parabola, then the vertical component is zero for an instant.)


Hint: what is the definition of acceleration? :smile:


I know the definition of acceleration is the slope of the v(t) graph, but does that definition still hold true for a ball going up and coming down? And that acceleration would be negative right? It just doesn't seem like the acceleration would be constant all the way through.
 
  • #4
1)
For simplicity, imagine the object is thrown upwards at a rate of exactly g. After one second, it will "decelerate" by exactly acceleration due to gravity (1sec*g=g.) -- that is, after one second it will come to a complete stop. Now what happens if we wait 1.001 seconds? Obviously it won't be EXACTLY at a stand still. Hence it only stops for an instant.
 
  • #5
physics213 said:
I know the definition of acceleration is the slope of the v(t) graph, but does that definition still hold true for a ball going up and coming down? And that acceleration would be negative right?
It just doesn't seem like the acceleration would be constant all the way through.

When the line of the velocity graph is above the x-axis, the ball is rising.

When it is below the x-axis, the ball is falling.

But it's an unbroken line … it goes through the x-axis "without blinking"!

The acceleration, as measured on the line, is the same whether the velocity is positive or negative … which matches the constant acceleration which you know gravity has. :smile:
 

What are motion graphs?

Motion graphs are visual representations of an object's motion over time. They show the relationship between an object's position, velocity, and acceleration.

What types of motion graphs are there?

There are three types of motion graphs: position-time graphs, velocity-time graphs, and acceleration-time graphs. Each type shows a different aspect of an object's motion.

How do you read a motion graph?

In a position-time graph, the object's position is shown on the y-axis and time is shown on the x-axis. The slope of the line represents the object's velocity. In a velocity-time graph, the object's velocity is shown on the y-axis and time is shown on the x-axis. The slope of the line represents the object's acceleration. In an acceleration-time graph, the object's acceleration is shown on the y-axis and time is shown on the x-axis. The area under the line represents the change in velocity.

What is the difference between distance and displacement in a motion graph?

Distance is the total length traveled by an object, while displacement is the straight-line distance from the starting point to the ending point. In a motion graph, distance is represented by the total area under the line, while displacement is represented by the final position on the y-axis.

Can you use motion graphs to predict future motion?

Yes, motion graphs can be used to predict an object's future motion based on its current position, velocity, and acceleration. By analyzing the trend of the graph, you can make predictions about how the object will continue to move in the future.

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