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Watch this video to learn how to interpret position vs. time graphs and how they relate to displacement, velocity, and speed. You will see examples of different types of motion and how to calculate the slope of the graph. This is a key skill for understanding one-dimensional motion in physics.
- 15 min
- David SantoPietro
- Because it leaves room for the graph to fail the vertical line test. Then it would not longer be a function; rather an inverse function.
- Yeah, I was going to mention this in the video but it got a little long. It is really unfortunate that the horizontal (independent variable) is alw...
- The function isn't differentiable at that point, because the functions is switching sides. This is because the left derivative and the right deriva...
- A1: 3m from an arbitrary point in space. for example it could be 3m from a starting line on a track. A2. From center of mass (note the white line t...
- No. Distance-vs.-time graphs only account for the total movement over time. Position-vs.-time graphs note one's position relative to a reference po...
- You will have to use a derivative function from calculus.
- "_At both 2 seconds and 4 seconds, the limits of the graph exist, but not the limits of the slopes at those points (am I stating this part correctl...
- Well.. Its actually position.. But yeah u can say that its the distance from zero.. i.e origin .. For eg.. when the the turtle is at 3 . it means t...
- It has a same unit but Velocity is vector while Speed is scalar. If you talk about Velocity, it's a vector, you need to know both magnitude and dir...
The graph of position versus time in Figure 2.13 is a curve rather than a straight line. The slope of the curve becomes steeper as time progresses, showing that the velocity is increasing over time. The slope at any point on a position-versus-time graph is the instantaneous velocity at that point.
- Overview
- How are position vs. time graphs useful?
- What does the vertical axis represent on a position graph?
- What does the slope represent on a position graph?
- What does the curvature on a position graph mean?
- Example 1: Hungry walrus
- Example 2: Happy bird
See what we can learn from graphs that relate position and time.
How are position vs. time graphs useful?
Many people feel about graphs the same way they do about going to the dentist: a vague sense of anxiety and a strong desire for the experience to be over with as quickly as possible. But position graphs can be beautiful, and they are an efficient way of visually representing a vast amount of information about the motion of an object in a conveniently small space.
What does the vertical axis represent on a position graph?
The vertical axis represents the position of the object. For example, if you read the value of the graph below at a particular time you will get the position of the object in meters.
Try sliding the dot horizontally on the graph below to choose different times and see how the position changes.
Many people feel about graphs the same way they do about going to the dentist: a vague sense of anxiety and a strong desire for the experience to be over with as quickly as possible. But position graphs can be beautiful, and they are an efficient way of visually representing a vast amount of information about the motion of an object in a convenient...
The vertical axis represents the position of the object. For example, if you read the value of the graph below at a particular time you will get the position of the object in meters.
Try sliding the dot horizontally on the graph below to choose different times and see how the position changes.
Concept check: What is the position of the object at time t=5 seconds according to the graph above?
The slope of a position graph represents the velocity of the object. So the value of the slope at a particular time represents the velocity of the object at that instant.
To see why, consider the slope of the position vs. time graph shown below:
[Wait, why is the vertical axis called x?]
The slope of this position graph is slope=riserun=x2−x1t2−t1 .
This expression for slope is the same as the definition of velocity: v=ΔxΔt=x2−x1t2−t1 . So the slope of a position graph has to equal the velocity.
This is also true for a position graph where the slope is changing. For the example graph of position vs. time below, the red line shows you the slope at a particular time. Try sliding the dot below horizontally to see what the slope of the graph looks like for particular moments in time.
Look at the graph below. It looks curvy since it's not just made out of straight line segments. If a position graph is curved, the slope will be changing, which also means the velocity is changing. Changing velocity implies acceleration. So, curvature in a graph means the object is accelerating, changing velocity/slope.
On the graph below, try sliding the dot horizontally to watch the slope change. The first hump between 1 s and 5 s represents negative acceleration since the slope goes from positive to negative. For the second hump between 7 s and 11 s , the acceleration is positive since the slope goes from negative to positive.
Concept check: What is the acceleration of the object at t=6 s according to the graph above?
[Show me the answer.]
To summarize, if the curvature of the position graph looks like an upside down bowl, the acceleration will be negative. If the curvature looks like a right side up bowl, the acceleration will be positive. Here's a way to remember it: if your bowl is upside down all your food will fall out and that is negative. If your bowl is right side up, all your food will stay in it and that is positive.
Finding the velocity at 2 s :
We can find the velocity of the walrus at t=2 s by finding the slope of the graph at t=2 s : slope=x2−x1t2−t1(use the formula for slope) Now we will pick two points along the line we are considering that conveniently lie at a hashmark so we can determine the value of the graph at those points. We'll choose the points (0 s,1 m) and (4 s,3 m) , but we could pick any two points between 0 s and 4 s . We must plug in the later point in time as point 2, and the earlier point in time as point 1. slope=3 m−1 m4 s−0 s(Pick two points and plug the x values into the numerator and the t values into the denominator.) slope=2 m4 s=12 m/s(Calculate and celebrate.) So, the velocity of the walrus at 2 s was 0.5 m/s .
Finding the velocity at 5 s :
To find the velocity at 5 s , we just have to note that the graph is horizontal there. Since the graph is horizontal, the slope is equal to zero, which means that the velocity of the walrus at 5 s was 0 m/s .
Finding the velocity at 8 s :
slope=x2−x1t2−t1(Use the formula for slope.) We'll pick the points at the beginning and end of the final line segment, which are (6 s,3 m) and (9 s,0 m) . slope=0 m−3 m9 s−6 s(Pick two points and plug the x values into the numerator and the t values into the denominator.) slope=−3 m3 s=−1 m/s(Calculate and celebrate.) So, the velocity of the walrus at 8 s was −1 m/s .
The motion of an extraordinarily jubilant bird flying straight up and down is given by the graph below, which shows the vertical position y as a function of time t . Answer the following questions about the motion of the bird.
What was the average velocity of the bird between t=0 s and t=10 s ?
Jan 11, 2021 · It’s easy to calculate the average velocity of a moving object from a position-time graph. Average velocity equals the change in position (represented by Δd) divided by the corresponding change in time (represented by Δt): velocity=Δd/Δt. For example, in Graph 2 in the Figure above, the average velocity between 0 seconds and 5 seconds is:
Sep 1, 2015 · If you know the initial position you can calculate the final position, otherwise, what you can calculate is only the change in position (ie, the displacement), but not the final position at the end of 3 sec. Initial position of 2.3 m gives a value for displacement from an unknown/unspecified origin but not the initial position. P. Radhakrishnamurty
Just as we could use a position vs. time graph to determine velocity, we can use a velocity vs. time graph to determine position. We know that v = d / t. If we use a little algebra to re-arrange the equation, we see that d = v × × t. In Figure 2.16, we have velocity on the y -axis and time along the x -axis.
People also ask
How do you find the velocity of a position graph?
How do you find the final position of a time graph?
How do you calculate position vs time?
How do you find instantaneous velocity in a position versus time graph?
We can find the change in velocity by finding the area under the acceleration graph. Δ v = area = b h = ( s) ( m s) = m/s (Use the formula for area of triangle: 1 2 b h) . Δ v = m/s (Calculate the change in velocity.) . But this is just the change in velocity during the time interval. We need to find the final velocity.
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