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How Does the Velocity-Distance Graph Relate to a Particle's Acceleration?
In summary, the conversation is about finding the solution to a problem involving the velocity and acceleration of a particle moving along the x-axis. The person asking for help has limited knowledge of differential equations and is studying motion in a straight line. The solution to the problem is given as 4x-8, but no explanation is provided. ChetSir guides them by asking for the equation for velocity and its derivative, and the person responds with their attempts and ultimately gets the solution with ChetSir's help.
- #2
- 23,586
- 5,826
Show us how you've analyzed the problem so far, please. Are you studying differential equations now?
Chet
Chet
- #3
sylwesh98
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Sir ,
I've tried the sum according to the following attachment .
Actually I have very less knowledge of differential equations.
I came across this problem when I'm studying motion in a straight line chapter.
The answer given is 4x-8
But no solution is given.
Please help me sir.
Thanks in advance!
I just wanted to know how to do the sum!
I've tried the sum according to the following attachment .
Actually I have very less knowledge of differential equations.
I came across this problem when I'm studying motion in a straight line chapter.
The answer given is 4x-8
But no solution is given.
Please help me sir.
Thanks in advance!
I just wanted to know how to do the sum!
Attachments
- #4
- 23,586
- 5,826
OK, from the graph, what is the equation for the velocity v as a function of the distance x? (This is the first step in obtaining the solution).sylwesh98 said:
Chet
- #5
sylwesh98
- 42
- 0
V=-2x+4
- #6
sylwesh98
- 42
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Even after trying with that equation I can't get the solution
- #7
- 23,586
- 5,826
Take the derivative of this equation with respect to time. What do you get? How is dv/dt related to the acceleration. How is dx/dt related to the velocity?sylwesh98 said:
Chet
- #8
sylwesh98
- 42
- 0
I got a=-2v and v = -2x +4 and solving them I got the answer
thank you sir!
thank you sir!
FAQ: How Does the Velocity-Distance Graph Relate to a Particle's Acceleration?
What is a velocity versus distance graph?
A velocity versus distance graph is a visual representation of the relationship between an object's velocity and the distance it has traveled. The velocity is typically shown on the y-axis and the distance on the x-axis.
How is velocity calculated on a velocity versus distance graph?
Velocity is calculated by finding the slope of the line on the graph. The slope represents the change in distance over the change in time, which is the definition of velocity. The steeper the slope, the greater the velocity of the object.
What can a velocity versus distance graph tell us about an object's motion?
A velocity versus distance graph can tell us about the speed and direction of an object's motion. It can also show us if the object is accelerating, decelerating, or moving at a constant velocity.
How does the shape of a velocity versus distance graph indicate an object's motion?
If the graph has a positive slope, it means the object is moving in a positive direction and increasing in velocity. If the slope is negative, the object is moving in a negative direction and decreasing in velocity. A flat line indicates a constant velocity, and a curved line indicates changing velocity.
What are some real-world applications of a velocity versus distance graph?
A velocity versus distance graph is commonly used in physics and engineering to analyze the motion of objects, such as vehicles, projectiles, and machines. It is also used in sports, such as track and field, to track an athlete's speed and progress. Additionally, it can be used in transportation planning to optimize travel times and routes.