Question

1. [6 Points] A particle is moving along the x-axis. It starts from rest at x = 0 and moves to x = L under the action of a variable force with an x-component given by F(x): x2 if 0 SXSL F(x) = 3 L2 Lx if LSX <3L 1 Everything is in SI units: x in meters and F in Newtons. Part 1: What is the particle's kinetic energy at x = L? Express your answer in terms of L and F. (2 pts) K(x = Part 2: What is the particle's kinetic energy at x = 3L? Express your answer in terms of L and F. (2 pts) K (x = L) = Part 3: If the mass of the particle is 2 kg and L = 3 meters, what is the speed of the particle at x = 3L? (2 pts) V=

Answer 1

The first step is to set the equations for energy -- this time kinetic energy -- and work equal to each other and solve for force. W = KE is F × d = 0.5 × m × v^2, so F = (0.5 × m × v^2) ÷ d.

Part 1

So to calculate the Kinetic energy at x = L

K.E = F * d

F at x = l is given by x*x

so substituting we get :

K.E. = x*x*L =  (x^​2 )* L or Fo *L

Part 2.

F at x = 3L is given by 3/2 L^2 - 1/2Lx

so substituting we get :

K.E. = (3/2 L^2 - 1/2Lx ) * 3L or Fo * 3L

K.E. = 9/2 L^3 -3/2 (L^2* x) or   Fo * 3L

Part 3.

We know that the equation for K.E at x = 3l is

K.E. = 9/2 L^3 -3/2 (L^2* x)

Finding it :

L= 3m

x =3L = 9 m

m= 2kg

So substituing and solving we get

K.E = 81 kgm/s^2

Also K.E = 0.5 × m × v^2

81 = 0.5 * 2 * v^2

v^ 2 = 81 /1 = 81

v = sqrt (81)

v = 9 m/s

P.S.If this helped you please like the answer.Thankyou.