What does the shape of the position-time graph reveal?
The shapes of the position versus time graphs for these two basic types of motion - constant velocity motion and accelerated motion (i.e., changing velocity) - reveal an important principle. The principle is that the slope of the line on a position-time graph reveals useful information about the velocity of the object.
What does the curvature of a position graph mean?
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.
Why is the slope of a position time graph important?
The Importance of Slope. The shapes of the position versus time graphs for these two basic types of motion - constant velocity motion and accelerated motion (i.e., changing velocity) - reveal an important principle. The principle is that the slope of the line on a position-time graph reveals useful information about the velocity of the object.
What does a curved line on a velocity graph mean?
In either case, the curved line of changing slope is a sign of accelerated motion (i.e., changing velocity). 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 ).
What do curved graphs mean?
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.e., changing velocity).
What does curved velocity time graph represent?
The slope of a velocity graph represents the acceleration of the object. So, the value of the slope at a particular time represents the acceleration of the object at that instant.
What does a curved line represent on a distance vs time graph?
Note: Curved lines on a distance-time graph indicate that the speed is changing.
What will you conclude if velocity time graph is a curve?
Example: If the acceleration of a particle is a function of time and the initial velocity is zero, the velocity-time graph will be a curve. The slope of the velocity-time graph at any instant (at a certain time) will give the acceleration at that time.
Can a speed time graph be curved?
Since acceleration is a function of time, speed time graph will be a curve.
How do you read a position time graph?
A position- time graph shows how far an object has traveled from its starting position at any given time since it started moving. The steeper the line is, the greater the slope of the line and the faster the object's motion is changing.
What does a line curving upwards on a?
A curved line on a distance-time graph represents acceleration or deceleration. For the given figure, it is acceleration. When studying the motion of bodies, we deal with the distance-time graphs. The distance-time graphs are used to represent a body's motion.
How do you find the distance on a curved velocity time graph?
0:1246:31Curved Distance & Velocity Time Graphs - YouTubeYouTubeStart of suggested clipEnd of suggested clipWith a gradient by difference in distance divided by difference in time. We can calculateMoreWith a gradient by difference in distance divided by difference in time. We can calculate acceleration by doing difference in speed divided by difference in time.
What does a linear graph indicate about the acceleration of rolling objects?
What does a linear graph indicate about the acceleration of rolling objects? A linear graph indicates that the acceleration of rolling objects is constant and stays the same.
How do you find the distance on a curved velocity-time graph?
0:1246:31Curved Distance & Velocity Time Graphs - YouTubeYouTubeStart of suggested clipEnd of suggested clipWith a gradient by difference in distance divided by difference in time. We can calculateMoreWith a gradient by difference in distance divided by difference in time. We can calculate acceleration by doing difference in speed divided by difference in time.
How do you find the area under a curve on a velocity-time graph?
0:153:05Area Under Velocity Time Graphs | Forces & Motion | Physics - YouTubeYouTubeStart of suggested clipEnd of suggested clipLet's start by looking at a simple velocity time graph to find the area underneath the line multiplyMoreLet's start by looking at a simple velocity time graph to find the area underneath the line multiply the value on the horizontal axis with the value on the vertical. Axis.
What is the slope on velocity-time graph?
The slope of a velocity graph represents an object's acceleration. As a result, the value of the slope at a given time represents the object's acceleration at that time. The rate of change of an object's velocity with respect to time is defined as acceleration.
Define Uniform Motion.
A body is said to be in uniform motion when it covers equal distance in equal interval of time within a precisely fixed direction.
What is uniformly accelerated motion?
A body is said to be in uniformly accelerated motion when its velocity increases by an equal amount in an equal interval of time while travelling i...
What does the slope of the position time graph represent?
The slope of the position time graph represents the velocity of an object.
What does a negative slope position-time graph represent?
Negative slope of a position-time indicates the velocity of an object moving in the opposite direction.
Is it possible that the position-time graph for the motion of an object be a vertical line?
A vertical line in a position-time graph would mean that an object is occupying more than one position at same time, hence, it is not possible.
What does a position-time graph tell you about the motion of the object?
There is more than just a position from a p-t graph, instead, it provides a lot of information.
How to find the instantaneous slope of a graph?
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 line.
How to represent the position of a moving body?
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 kilometreetc. is chosen to represent the position. 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 xtor x(t) at any instant t. Then, xtor x(t) is called as theposition 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).
How to find velocity from 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. That is, the average slope along a line that doesn’t change its slope will give us the average velocity in that line and the instantaneous slope of the graph will give us the instantaneous velocity.
What does changing velocity mean?
Changing velocity means an accelerating object. We know, the slope of the position-time graph will give us the velocity, and an accelerating object will have a changing slope. Here, the p-t graph of object D is a curve which means it is having a changing slope and hence object D is accelerating.
What is non uniform motion?
For non-uniform motion, the object is changing its velocity throughout the motion. i.e., the object covers an unequal distance in equal intervals of time. The position-time graph of a body moving with non-uniform velocity will be curved and may have many changes in its direction.
What is the total average velocity of a graph?
Similarly, the total average velocity for this graph = total displacement/time = 0/11 = 0 m/s , means the total average velocity for the entire motion shown in this graph is zero because the object has no displacement here.
What information should be included in a description of an object?
In your description, be sure to include such information as the direction of the velocity vector (i.e., positive or negative), whether there is a constant velocity or an acceleration, and whether the object is moving slow, fast, from slow to fast or from fast to slow. Be complete in your description. See Answer to A.
What does a curved line mean on a graph?
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.e., changing velocity).
What is the slope of a position versus time graph?
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." Whatever characteristics the velocity has, the slope will exhibit the same (and vice versa). If the velocity is constant, then the slope is constant (i.e., a straight line). If the velocity is changing, then the slope is changing (i.e., a curved line). If the velocity is positive, then the slope is positive (i.e., moving upwards and to the right). This very principle can be extended to any motion conceivable.
What is the lesson 3 of kinematics?
Lesson 3 focuses on the use of position vs. time graphs to describe motion. 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. time graph. 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.
Why is slope important in a graph?
The principle of slope is an incredibly useful principle for extracting relevant information about the motion of objects as described by their position vs. time graph. Once you've practiced the principle a few times, it becomes a very natural means of analyzing position-time graphs.
Is the graph on the right a velocity?
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.
Is the slope constant or changing?
If the velocity is constant, then the slope is constant (i.e., a straight line). If the velocity is changing, then the slope is changing (i.e., a curved line).
How are position vs. time graphs useful?
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.
What does the curvature on a position graph mean?
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.
What do solved examples involving position vs. time graphs look like?
The motion of a hungry walrus walking back and forth horizontally looking for food is given by the graph below, which shows the horizontal position as a function of time .
What does curvature mean in a graph?
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 and represents negative acceleration since the slope goes from positive to negative.
What does the slope of a position graph give you?
One more thing to keep in mind is that the slope of a position graph at a given moment in time gives you the instantaneous velocity at that moment in time. The average slope between two points in time will give you the average velocity between those two points in time.
What happens if the position graph looks like an upside down bowl?
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.
What happens when you jump on a velocity graph?
But in addition, the instantaneous jump on the velocity graph from 2 m/s to 0 m/s becomes a smooth, slanted line with a large negative slope instead of a vertical line.
What does it mean when the velocity of a graph is zero?
Of course, if her velocity is zero, that means there should be no curve on the graph over that time interval. In other words, the curve is now directly on top of the x-axis.
What does negative velocity mean?
Remember, a negative velocity does not mean slowing down (that's negative acceleration). It means moving in the negative direction! Altogether, that means the velocity-time graph for the last segment of her ride ( t = 8 to t = 15) needs to show a straight line where her velocity is growing negatively .
What is the slope of a position time graph?
Position-time graphs lead directly to velocity-time graphs: The slope of a position-time line shows the velocity of the object in the same time interval. This makes sense because position vs. time is just another way of saying meters per second – the definition of velocity.
What is the y axis on a graph?
The y-axis on each graph is position in meters, labeled x (m); velocity in meters per second, labeled v (m/s); or acceleration in meters per second squared, labeled a (m/s 2)
Why do we use graphs?
Each of these graphs helps to tell the story of the motion of an object. Moreover, when the position, velocity and acceleration of an object are graphed over the the same time interval, the shapes of each graph relate in a specific and predictable way.
What does a steep curve do on an acceleration graph?
On the acceleration graph, at around the five second mark, a steep curve would dip into the negative region before coming back to 0 to indicate the negative acceleration required to come to a stop. And the jump that occurs at the 8 second mark, instead of being vertical, would simply curve into a line with a large negative slope that then smoothly flattens out at -0.5 m/s/s.
