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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 xinitial=l to xfinal=3l. what is δk, the change in kinetic energy of the particle during that time? express your answer in terms of c and l.

Respuesta :

skyluke89
The work-energy theorem states that the change in kinetic energy of the particle is equal to the work done on the particle:
[tex]\Delta K = W[/tex]
The work done on the particle is the integral of the force on dx:
[tex]W= \int\limits^{3L}_L {F(x)} \, dx = \int\limits^{3L}_L {cx^2} \, dx = \frac{26}{3}cL^3 [/tex]
So, this corresponds to the change in kinetic energy of the particle.
batolisis

The change in kinetic energy during that time is : [tex]\frac{26}{3} cl^{3}[/tex]

Given data :

Direction of particle = x

Net force = F(x) = cx²

Initial position = l

Final position = 3l

Determine the change in kinetic energy during this time

we will apply the work energy theorem which is : ΔK = W

To determine change in kinetic energy we have to determine the work done on the particle.

Work done on particle ( W ) =  [tex]\int\limits^3_l F({x}) \, dx[/tex] =  [tex]\int\limits^3_l c{x^{2} } \, dx =[/tex] [tex]\frac{26}{3} cl^{3}[/tex]

Hence the change in kinetic energy during that time is : [tex]\frac{26}{3} cl^{3}[/tex]

Learn more about work energy theorem : https://brainly.com/question/22236101

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