Question

"What is the value of the constant 'c' in the force F = (cx - 3.00x^2) i that acts on a particle as the particle moves along the x-axis, with F in newtons, x in meters, and c a constant, given that at x = 0, the particle's kinetic energy is 20.0 J, and at x = 3.00 m, it is 11.0 J?"

Answer 1

To find the value of the constant 'c' in the force equation F = (cx - 3.00x^2) i, we can use the information given about the particle's kinetic energy at different positions.

Step-by-step explanation:

To find the value of the constant 'c' in the force equation F = (cx - 3.00x^2) i, we can use the information given about the particle's kinetic energy at different positions. Kinetic energy (KE) is given by the formula KE = 1/2 mv^2, where m is the mass of the particle and v is its velocity. At x = 0, the kinetic energy is 20.0 J, so we can set up the equation 20 = 1/2 m (dx/dt)^2. Similarly, at x = 3.00 m, the kinetic energy is 11.0 J, so we have 11 = 1/2 m (dx/dt)^2. By solving these two equations, we can determine the value of 'c'.