The velocity vs. The shapes of the velocity vs. The principle is that the slope of the line on a velocity-time graph reveals useful information about the acceleration of the object. If the acceleration is zero, then the slope is zero i. If the acceleration is positive, then the slope is positive i.
If the acceleration is negative, then the slope is negative i. This very principle can be extended to any conceivable motion. The slope of a velocity-time graph reveals information about an object's acceleration. But how can one tell whether the object is moving in the positive direction i. And how can one tell if the object is speeding up or slowing down?
The answers to these questions hinge on one's ability to read a graph. Since the graph is a velocity-time graph, the velocity would be positive whenever the line lies in the positive region above the x-axis of the graph.
Similarly, the velocity would be negative whenever the line lies in the negative region below the x-axis of the graph. As learned in Lesson 1 , a positive velocity means the object is moving in the positive direction; and a negative velocity means the object is moving in the negative direction. So one knows an object is moving in the positive direction if the line is located in the positive region of the graph whether it is sloping up or sloping down.
And one knows that an object is moving in the negative direction if the line is located in the negative region of the graph whether it is sloping up or sloping down. And finally, if a line crosses over the x-axis from the positive region to the negative region of the graph or vice versa , then the object has changed directions.
Now how can one tell if the object is speeding up or slowing down? If we add them together, we see that the net displacement for the whole trip is 0 km, which it should be because we started and ended at the same place. This is good because it can tell us whether or not we have calculated everything with the correct units.
This process is called dimensional analysis, and it is one of the best ways to check if your math makes sense in physics. The area under a velocity curve represents the displacement. The velocity curve also tells us whether the car is speeding up.
In our earlier example, we stated that the velocity was constant. So, the car is not speeding up. Graphically, you can see that the slope of these two lines is 0.
This slope tells us that the car is not speeding up, or accelerating. We will do more with this information in a later chapter.
For now, just remember that the area under the graph and the slope are the two important parts of the graph. Just like we could define a linear equation for the motion in a position vs.
As we said, the slope equals the acceleration, a. And in this graph, the y -intercept is v 0. But what if the velocity is not constant? At the beginning of the motion, as the car is speeding up, we saw that its position is a curve, as shown in Figure 2. You do not have to do this, but you could, theoretically, take the instantaneous velocity at each point on this graph.
If you did, you would get Figure 2. Again, if we take the slope of the velocity vs. And, if we take the area under the slope, we get back to the displacement. Return to the scenario of the drive to and from school. Re-draw the V-shaped position graph. Ask the students what the velocity is at different times on that graph. Students should then be able to see that the corresponding velocity graph is a horizontal line at 0.
Then draw a few velocity graphs and see if they can get the corresponding position graph. Ask—Can a velocity graph be used to find the position? Can a velocity graph be used to find anything else? Ask students whether the velocity could actually be constant from rest or shift to negative so quickly. What would more realistic graphs look like? How inaccurate is it to ignore the non-constant portion of the motion? Also, the instantaneous velocity can be read off the velocity graph at any moment, but more steps are needed to calculate the average velocity.
Most velocity vs. When this is the case, our calculations are fairly simple. Use this figure to a find the displacement of the jet car over the time shown b calculate the rate of change acceleration of the velocity.
The average velocity we calculated here makes sense if we look at the graph. The quantities solved for are slightly different in the different kinds of graphs, but students should begin to see that the process of analyzing or breaking down any of these graphs is similar.
Ask—Where are the turning points in the motion? When is the object moving forward? What does a curve in the graph mean? Also, students should start to have an intuitive understanding of the relationship between position and velocity graphs. You can have negative position, velocity, and acceleration on a graph that describes the way the object is moving. You should never see a graph with negative time on an axis. Most of the velocity vs. Occasionally, we will look at curved graphs of velocity vs.
More often, these curved graphs occur when something is speeding up, often from rest. Use Figure 2. This is a much more complicated process than the first problem. To find the distance travelled, look at the area under the graph. Look at this velocity-time graph and answer the question. This question requires an extended response, ie your answer must be fairly long. Describe this journey in as much detail as possible. Give values for speeds, acceleration and distances travelled.
From 20 to 30 seconds the car decelerates or slows to a stop at 30 seconds. The mean speed of the vehicle over the whole journey is the total distance divided by the total time, ie. Velocity-time graphs of motion Velocity-time graphs Velocity-time graphs show how the velocity or speed of a moving object changes with time.
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