Position Time graph and what does it tells you
What does the movement shown on this graph represent? The output of goods and services. The theory of production deals with the relationship between the factors of production and? 9. Based on the graphs, what would be the market quantity of soccer balls supplied at a "P" of $20? 3 more. What does the movement shown on this graph represent the inverse relationship between price and quantity demanded The change from old demand curve to the new demand curve shown in the table represents a shift of the demand curve to the right.
By going through this article you will get a deep knowledge about the rhis graphs, how to draw the p-t graph, what information do they provide regarding the motion of the object, understand about the different shapes of p-t graph, finding the slope on a p-t graph, drawing the velocity-time graph from a position-time graph etc.
First, I am going to discuss the different ways to represent the change in position over time. One of the way to represent it is by using a table. From the table it is understood that for the time zero, one and two seconds, the position is at three metres, for the third and fourth seconds the position is at negative two metres, for the fifth and sixth seconds the position is at zero, and then the position is at two, one, negative three and two metres thf the time seven, eight, nine and ten seconds respectively.
Also, shiwn way of representation does not tell us what is happening in between these time intervals. That is, this table does not tell us the position of the object at time quarter of a second or half of a second. So for that, we can construct a thiz, representing the time on the horizontal axis and position over the vertical axis, known as the position-time graph. The corresponding position-time graph for the details provided in the above table can be drawn as shown below.
Usually, the X-axis is taken as the time axis and some instant of time is chosen as the origin and is assigned the value zero of time. A convenient unit of time like a second, minute, hour, day or year is chosen. The events that occurred before the origin of time are assigned negative values, while events after this are assigned positive values of the time.
Similarly, the position of a moving body can be represented graphically say, along with the Y—axis. A convenient unit of length like a centimetre, metre or kilometre etc. The position of the body above origin is taken as positive and that below origin is taken as negative. The position of the moving body is represented by a real number x t or x t at any instant t.
Then, x t or x t is called as the position coordinate. It can be a positive, a negative or a zero number. As said earlier, the graph between the position of an object at different instants of time and the corresponding time is called its position-time graph p-t graph. Again look at figure 1. For the time up to two seconds, there is no change in the position and the repreaent of the object is constant at three metres and can be represented as a horizontal straight line.
So a horizontal straight line in a how to get a nice big butt graph represents no motion or the object is stationary. As the object moves from the second to the third second, the position went from three to negative two at a constant rate and is represented again by a straight line, and similarly, the position for remaining time intervals can be drawn as shownn in the graph.
Similarly, we can represent the movement of a loaded spring, the movement of the needle of a sewing machine, a body thrown vertically upwards, etc. As said earlier, showwn graph is drawn by taking time along x-axis and position along the y-axis.
For a stationary object, its position will not change with time. So the graph of a stationary object is a straight line AB parallel to the x-axis as shown in the above figure 2. There is more than just a position from a p-t graph, instead, it provides a lot of information.
Let us discuss in detail about the things that can be obtained from the position-time graph with the help of the example shown in figure 3. The displacement between any two time instants can be found out from the p-t graph. For the example given in figure 3, the displacement between 2 seconds and 5 seconds can be calculated as follows. Here, the final position would be the position of the object at 5 second which is -3 metres and initial position would be the position of the object at 2 seconds which is 4 metres.
So here the object started and ended at the same point and hence the total displacement is zero. Next, we can find out the total dles or distance between any two points from the p-t graph shown in example figure 3. Remember, the total distance travelled will be the sum of all the path links travelled wht, all the path links should be taken as positive oj the distance is always positive and no need to consider its direction.
That means a total distance of 14 metres was travelled by the object for the whole trip. Similarly, the distance between any two points can be found out from the p-t graph. Next, we can figure out the average velocity. We know that average velocity is the displacement per time.
Here how to choose a financial planner final position is -3 metres at time 5 seconds and the initial position is 4 metres at time 3 seconds.
Similarly, we can find out the average speed what does the movement shown on this graph represent from the position versus time graph.
We know that the average speed is defined as the distance per time. We already found that the total distance covered by the object was 14 meters. That is, the object was moving at 1. That was its average speed. Similarly, we can find out the average speed between any two points. Now the most important part is we can find out the instantaneous velocity how can i make bittorrent download faster the p-t graph.
To find the instantaneous velocity from the p-t graph, you need to look at the slope. The slope of the position-time graph will give us the velocity in that direction. Here, we had a horizontal position-time graph and so the slope will give us the velocity in the x-direction. How can we find the instantaneous slope from a graph?
The lines in the graph are all straight lines. Therefore, the average slope between any two points on these lines is equal to the instantaneous slope at any point on that whah. Take any two points in that line and name it as point 1 and point 2. Any points can be chosen in this straight line, I choose these two points just because of convenience as I know exactly where they are at. So reading from the graph, at point 1 the horizontal position is 4 metres at time 3 seconds and at point 2 the position is —3 metres at time 5 seconds.
The same will get if you movdment the other two points in this line PQ. So we get the slope of the line PQ as So that was the instantaneous velocity at four seconds. Negative because the object was moving backwards. And since PQ is straight, this was the rate the object was moving at any moment between 3 and 5 seconds. That is, the instantaneous reptesent at 3. Similarly, the instantaneous velocity at 2 seconds or anywhere between 1 second and 3 seconds can be found out by taking the slope of the line PQ.
Similarly, the instantaneous velocity at 9 seconds or anywhere between 5 seconds thjs 11 seconds can be found out by taking the slope of the line RS. Positive because the object was moving forward. Lastly, we can figure out the instantaneous speed at a point from the p-t graph. The magnitude of instantaneous velocity at a point gives the instantaneous speed at that point, assuming the body is having motion in only one direction. For example, the instantaneous speed at 4 seconds is positive 3.
This would be the instantaneous speed at 4 seconds or any time between three to five seconds. This would be the instantaneous speed at 4 seconds or any time between five to eleven seconds. The value of the horizontal p-t graph gives the horizontal position of the object and the slope of the horizontal p-t graph gives the velocity in the x-direction. The average slope gives the average velocity in that line and the instantaneous slope gives the instantaneous velocity. Also, the magnitude of the instantaneous velocity gives how to set up a holding company uk instantaneous speed.
A particle is said to move with uniform velocity if it makes equal displacements in wht intervals of time. The position-time graph in uniform motion will be a straight line without any curve or bend as shown in the figure and the slope of the p-t graph gives the velocity of an object moving with uniform velocity. For non-uniform motion, the object is changing its velocity throughout the motion.
The position-time graph of a body moving with non-uniform velocity will be curved and may have many changes in its direction. We know, velocity is the gradient slope of the position-time graph. For a body moving with non-uniform velocity, the velocity of the body is always changing, which means the gradient of the curve is always changing.
The gradient of the curve is changing means the velocity is changing. The gradient or slope of a curve at any point is given by the gradient slope of the tangent at that point. A tangent is a straight how to make palo santo oil which touches the curve at one point only. The slope or gradient of a curve is different at each point on the curve.
By looking at the position-time graph, not only you can figure out exactly what the object is doing but you should be able to draw a velocity versus time graph from a position versus time graph. Consider the position-time graph given in the below figure By looking at the motion of the body from 0 to 3 second in the p-t graph given, it is clear that the object is at position 4 and it is not moving.
Similarly, it is already found in the previous section figure 4, section 2. So mark it also on the velocity-time graph. Similarly, the object is moving at a constant velocity of 1. You can see that the sshown waited for a period repreent time, then it moves at a constant velocity of Because if you figure out the slope of the position versus wuat graph that will always tell you the velocity versus time graph.
Similarly, if the body is moving at non-uniform velocity, the position in the p-t graph will be a curved line and then the slope can be found out by drawing the tangents on the curve and this will give the instantaneous velocity and by marking that velocities you can draw the velocity-time graph.
The direction of motion of the object can find out by finding the starting and ending the displacement of the object. Here the initial position is 7. So the object is moving in the negative direction. If the gradient is getting flatter, the object is slowing how to link spreadsheets in excel 2010 and if the gradient is getting steeper, the object is speeding up.
The tangent of the curve can be drawn as shown in the figure. From the figure, it is clear that the gradient is getting flattered and flatter, which means the object is slowing down. So, here the object is moving in the negative direction and is getting sown as time increases from 0 to 7 seconds. Here also, we can what does the movement shown on this graph represent the motion of the object in the same way as said above in the previous problem.
The position-time graph in uniform motion will be a straight line without any curve or bend as shown in the figure and the slope of the p-t graph gives the velocity of an object moving with uniform velocity. A positive slope on a position-time graph means that the object’s position from the origin is increasing with respect to time. Fig. 5. How does the graph represent movement to the left? How is the progress of the longitudinal waves shown on the displacement graph? _____ It is shown by the waves going from left / right and back again_ _____ _____ 7. Explore: Click Reset. Experiment with different values for the Strength and Freq. of the tuning fork. A. How. The movement shown in this graph represents a change in what? b. demand. A demand schedule shows. d. a listing of the various quantities demanded of a particular product at all prices that might prevail in the market. Consumers' willingness to replace a .
Our study of 1-dimensional kinematics has been concerned with the multiple means by which the motion of objects can be represented. Such means include the use of words, the use of diagrams, the use of numbers, the use of equations, and the use of graphs.
Lesson 3 focuses on the use of position vs. As we will learn, the specific features of the motion of objects are demonstrated by the shape and the slope of the lines on a position vs. The first part of this lesson involves a study of the relationship between the shape of a p-t graph and the motion of the object. If the position-time data for such a car were graphed, then the resulting graph would look like the graph at the right.
Note that a motion described as a constant, positive velocity results in a line of constant and positive slope when plotted as a position-time graph.
Note that a motion described as a changing, positive velocity results in a line of changing and positive slope when plotted as a position-time graph. The position vs. The shapes of the position versus time graphs for these two basic types of motion - constant velocity motion and accelerated motion i.
The principle is that the slope of the line on a position-time graph reveals useful information about the velocity of the object. It is often said, "As the slope goes, so goes the velocity. If the velocity is constant, then the slope is constant i. If the velocity is changing, then the slope is changing i. If the velocity is positive, then the slope is positive i. This very principle can be extended to any motion conceivable. Consider the graphs below as example applications of this principle concerning the slope of the line on a position versus time graph.
The graph on the left is representative of an object that is moving with a positive velocity as denoted by the positive slope , a constant velocity as denoted by the constant slope and a small velocity as denoted by the small slope.
The graph on the right has similar features - there is a constant, positive velocity as denoted by the constant, positive slope. However, the slope of the graph on the right is larger than that on the left.
This larger slope is indicative of a larger velocity. The object represented by the graph on the right is traveling faster than the object represented by the graph on the left.
The principle of slope can be used to extract relevant motion characteristics from a position vs. As the slope goes, so goes the velocity. Consider the graphs below as another application of this principle of slope. The graph on the left is representative of an object that is moving with a negative velocity as denoted by the negative slope , a constant velocity as denoted by the constant slope and a small velocity as denoted by the small slope.
The graph on the right has similar features - there is a constant, negative velocity as denoted by the constant, negative slope. Once more, this larger slope is indicative of a larger velocity. As a final application of this principle of slope, consider the two graphs below. Both graphs show plotted points forming a curved line. Curved lines have changing slope; they may start with a very small slope and begin curving sharply either upwards or downwards towards a large slope.
In either case, the curved line of changing slope is a sign of accelerated motion i. Applying the principle of slope to the graph on the left, one would conclude that the object depicted by the graph is moving with a negative velocity since the slope is negative. Furthermore, the object is starting with a small velocity the slope starts out with a small slope and finishes with a large velocity the slope becomes large.
That would mean that this object is moving in the negative direction and speeding up the small velocity turns into a larger velocity. This is an example of negative acceleration - moving in the negative direction and speeding up.
The graph on the right also depicts an object with negative velocity since there is a negative slope. The object begins with a high velocity the slope is initially large and finishes with a small velocity since the slope becomes smaller. So this object is moving in the negative direction and slowing down. This is an example of positive acceleration.
The principle of slope is an incredibly useful principle for extracting relevant information about the motion of objects as described by their position vs.
Once you've practiced the principle a few times, it becomes a very natural means of analyzing position-time graphs. Use the principle of slope to describe the motion of the objects depicted by the two plots below. In your description, be sure to include such information as the direction of the velocity vector i. Be complete in your description.
The object has a changing velocity note the changing slope ; it is accelerating. The object is moving from slow to fast since the slope changes from small big. The object has a negative or leftward velocity note the - slope.
The object has a changing velocity note the changing slope ; it has an acceleration. The object is moving from slow to fast since the slope changes from small to big.
Physics Tutorial. What Can Teachers Do My Cart Subscription Selection. Student Extras. Time Graphs. See Answer to B The object has a negative or leftward velocity note the - slope. Time Graphs » Meaning of Shape for a p-t Graph.