What is the velocity of the body

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The discussion focuses on calculating the velocity of a 3.4 kg body under the influence of a variable force, Fx = -6x N, as it moves along the positive x-axis. To find the velocity at x = 4.0 m, participants suggest using the work-energy principle, linking work done by the force to changes in kinetic energy. The body’s initial velocity at x = 3.0 m is given as 8.0 m/s, and the challenge involves deriving the velocity at a new position and determining where the velocity will reach 5.0 m/s. Newton's second law is referenced to establish a relationship between force, mass, and acceleration, indicating that the force varies with position. The conversation emphasizes the need to integrate these concepts to solve for the desired velocities.
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The only force acting on a 3.4 kg body as it moves along the positive x-axis has an x component Fx = - 6x N, where x is in meters. The velocity of the body at x = 3.0 m is 8.0 m/s.

a) What is the velocity of the body at x = 4.0 m? m/s

(b) At what positive value of x will the body have a velocity of 5.0 m/s?
i have some kinda idea but it may not be clear
so i started with using a Formula for work since its moving along positive x direction
W=Fd cos(angle)
and kinetic energy is
K=1/2mv^2
thats all i can think off for the beginning
Plz just give me some hint how to combine these 2 formulas since angle between force and direction is 180 it will be cos180
 
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Your force is varying with x.

So if the only force acting is Fx= 6x, can you use Newton's second law to find an expression for velocity?

(Hint: dv/dt = dv/dx * dx/dt)
 
still don't get it
 
nmegabyte said:
still don't get it

F= ma

-6x = ma
 

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