How to graph velocity where there is a change in acceleration

In summary, the conversation discusses the concepts of speed, velocity, acceleration, and distance vs time graphs. The problem being discussed involves a car moving at a constant speed of 20m/s for 100m and then stopping at a constant acceleration of 6m/s/s. There is confusion about the relationship between speed and velocity, and how to graph velocity and acceleration over time. The equations used to solve the problem are also discussed.
  • #1
Kerrie yu
11
0
The speed is a constant of 20m/s for 100m (moving on a straight line) after 100m, the car stops at a constant 6m/s/s.
*So in this case, speed is equal to velocity?
*How do you graph velocity vs time graph and acceleration vs time graph?
 
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  • #2
The problem statement tells you specifically how the acceleration is varying with time. What is your quantitative understanding of this?
 
  • #3
But first I need to know if constant speed is equal to velocity. So if there is a constant speed of 20m/s , is it mean that the velocity is constant 20m/s ?
 
  • #4
The problem implies that this is the case.

Chet
 
  • #5
So for the displacement vs time graph, the line would be going up from 0 to 100 ( take 5 sec) and then from 6 sec, it starts going down by 6 because of the acceleration. 5s=100m, 6s=94m and so on?
 
  • #6
Kerrie yu said:
So for the displacement vs time graph, the line would be going up from 0 to 100 ( take 5 sec) and then from 6 sec, it starts going down by 6 because of the acceleration. 5s=100m, 6s=94m and so on?
From 0 to 5 sec., this is correct. After five seconds, it is incorrect.

What equations are you using? If you had followed the PF template, you would have written down your equations in advance, and it would have been easier to help you. Please write down your equations.

Chet
 
  • #7
The second one? Df=...
 

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  • #8
Kerrie yu said:
The second one? Df=...
Yes, but you would have to restart the application of the equation after the first 5 seconds, so d in the equation would be the distance relative to the location after 5 seconds, and t in the equation would be 0 at the running time of 5 seconds.

Hope this makes sense. Now, what do you get?

Chet
 
  • #9
So we r starting new after 5sec? Df=100 ,vi=20, tf=0 ,a= -6 substitute these numbers?
 
  • #10
Wait no,,, di =100 , df is unknown
 
  • #11
..wait ..so since I am starting another one,, everything before 5sec doesn't matter,, so my vi is not 20m/s anymore?
 
  • #12
You seem to be pretty confused. But, you are beginning to get the right idea.

I might be better to think of this as two separate problems:

Problem 1:
Applies between time 0 and 5 seconds
Initial distance = 0
Velocity = 20 meters/sec
Acceleration = 0

You have already solved problem 1 correctly

Problem 2
Applies after 5 seconds
Initial distance = 100
Initial velocity = 20
Acceleration = -6

You need to modify your equations a little to handle this part:

v = 20 - 6t'
d = 100 + 20t'-6(t')2/2
where t'=(t-5)

So,

v = 20 - 6(t-5)
d = 100 + 20(t-5) - 6(t-5)2/2

Do these equations make sense to you?

Chet
 

Related to How to graph velocity where there is a change in acceleration

1. How do I graph velocity when there is a change in acceleration?

To graph velocity when there is a change in acceleration, you will need to plot the velocity on the y-axis and time on the x-axis. Then, use the slope or steepness of the line to represent the acceleration. A steeper line indicates a greater change in velocity over time, while a flatter line indicates a smaller change in velocity over time.

2. Can I use the same method to graph acceleration?

Yes, you can use the same method to graph acceleration. However, instead of plotting velocity on the y-axis, you will plot acceleration. The slope of the line will still represent the change in acceleration over time.

3. What if the acceleration is changing at a non-constant rate?

If the acceleration is changing at a non-constant rate, the graph will not be a straight line. Instead, it will be a curved line, with the slope changing at different points. To accurately graph this type of motion, you can break it down into smaller sections and plot the velocity and acceleration for each section separately.

4. How does a change in acceleration affect the velocity graph?

A change in acceleration will affect the velocity graph by changing the slope of the line. If the acceleration increases, the slope will become steeper, indicating a greater change in velocity over time. If the acceleration decreases, the slope will become flatter, indicating a smaller change in velocity over time. If the acceleration is constant, the line will be a straight diagonal line.

5. Can I use a graph to determine the velocity and acceleration at a specific time?

Yes, you can use a graph to determine the velocity and acceleration at a specific time. To do this, you can use the slope of the line at that specific point. The slope represents the change in velocity over time, so you can use it to calculate the acceleration. You can also determine the velocity by finding the y-coordinate of the point on the graph at that specific time.

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