Find the constant c given quadratic equation F=

In summary, the conversation discusses the relationship between force and kinetic energy, specifically in the context of a particle moving along an x-axis. The force is represented by F=(cx-3.00x2)i, with F in Newtons, x in meters, and c as a constant. At x = 0 m, the particle's kinetic energy is 18 J, and at x = 5 m, it is 12 J. To find c, the participants suggest using the equations F = ma and KE = 1/2mv2 and considering the work done by the force, which is equal to the change in kinetic energy. This leads to a differential equation relating F(x) to v and dv/dx, which
  • #1
rockchalk1312
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A force F=(cx-3.00x2)i acts on a particle as the particle moves along an x axis, with F in Newtons, x in meters, and c a constant. At x = 0 m, the particle's kinetic energy is 18 J; at x = 5 m, it is 12 J. Find c.

F=ma
KE=1/2mv2

I guess I don't understand the relationship between force and kinetic energy...
 
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  • #2
Hint: The work done by the force is equal to the change in kinetic energy.

How is Work Done by a force defined in terms of an integral?
 
  • #3
F = ma = dv/dt
Use chain rule to get from dv/dt to dv/dx
Come up with the differential equation relating F(x) to v and dv/dx
Solve. This results in a constant of integration plus you will still have c in the equation.
So, need 2 equations since you have 2 unknowns. Use the given boundary conditions to solve for both constants.
 

FAQ: Find the constant c given quadratic equation F=

What is the constant c in a quadratic equation?

The constant c in a quadratic equation represents the y-intercept, or the point where the parabola crosses the y-axis. It is the value of the equation when x=0.

How do I find the constant c given a quadratic equation?

To find the constant c, you can set the equation equal to 0 and solve for c. Alternatively, you can use the vertex form of a quadratic equation, which is F(x) = a(x-h)^2 + k, where h and k represent the x and y coordinates of the vertex respectively. The constant c is then equal to k.

Can the constant c be negative in a quadratic equation?

Yes, the constant c can be negative in a quadratic equation. This means that the parabola will have a y-intercept that is below the x-axis, resulting in a downward facing parabola.

What does the value of the constant c represent in a quadratic equation?

The value of the constant c represents the vertical shift of the parabola. A positive value of c will shift the parabola upwards, while a negative value will shift it downwards.

Is the constant c the same as the coefficient of x squared in a quadratic equation?

No, the constant c is not the same as the coefficient of x squared in a quadratic equation. The coefficient of x squared, represented by the variable a, determines the steepness of the parabola, while the constant c determines the vertical shift.

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