Aforce F, acts on a partide that has a mass of i5kg. The force is related to the

Question

Aforce F, acts on a partide that has a mass of i5kg. The force is related to the position x of the particle by the formula F- Newtons. where C-OS its n meters and risin (a)What are the SI units of C? (Use the following as necessary: N and m.) (b) Find the work W done by this force as the particle moves from x -3.9 m to x- 1.1 m (c) At x 1.1 m the force points opposite the direction of the particle's velocity (speed is 12 m/s). What is its speed at 3.9 m Vs.om Can you tell its direction of motion at x -3.9 m using only the work-kinetic energy theorem? m/s yes Explain.

Explanation / Answer

given function

F = C x^3

kg*m/s^2 = C * m^3

C= kg/(m^2*s^2)

(b)

the equation for workdone is

W = integral F(x) dx

= integral C x^3 dx

=0.5 x^4/ 4

wordone between x = 1.1 to 3.9

W = ( 0.5( 3.9)^4/4 ) - ( 0.5 ( 1.1^4)/ 4

=28.73 J

(c)

W= 1/2 m ( vf^2 - vi^2)

28.73= 1/2 * 1.5 ( vf^2 - 12^2)

= 13.5 m/s

(c)

No , the function  f(x) in not in vector form so we do not know the direction it is pointing.

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