How Does the Velocity-Distance Graph Relate to a Particle's Acceleration?

[sylwesh98]

Homework Statement

the velocity of a particle moving along x-axis varies with its position x as shown in figure. The acceleration of a particle varies with position as !

 

[Chestermiller]

Show us how you've analyzed the problem so far, please. Are you studying differential equations now?

Chet

 

[sylwesh98]

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!

 

[Chestermiller]

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!

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).

Chet

 

[sylwesh98]

V=-2x+4

 

[sylwesh98]

Even after trying with that equation I can't get the solution

 

[Chestermiller]

V=-2x+4

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?

Chet

 

[sylwesh98]

I got a=-2v and v = -2x +4 and solving them I got the answer
thank you sir!