A particle moving in the x direction is being acted upon by a net force F(x)=Cx2, for some constant C. The particle moves from xi=L to xf=3L. What is ΔK, the change in kinetic energy of the particle during that time?

Change in kinetic energy is ( 26CL³)/3

Explanation:

Given :

Net force applied, F(x) = Cx²  ....(1)

Displacement of the particle from xi = L to xf = 3L.

The work-energy theorem states that change in kinetic energy of the particle is equal to the net amount of work is done to displace the particle.

That is,

ΔK = W = ∫F·dx

Substitute equation (1) in the above equation.

ΔK =  ∫Cx²dx

The limit of integration from xi = L to xf = 3L, so

Substitute the values of xi and xf in the above equation.

the second one and the forth one are in the purple because they are opinions and the rest are in the yellow

explanation: