Question

A force ModifyingAbove Upper F With right-arrow equals left-parenthesis c x minus 3.00 x squared right-parenthesis ModifyingAbove i With ˆ acts on a particle as the particle moves along an x axis, with ModifyingAbove Upper F With right-arrow in newtons, x in meters, and c a constant. At x = 0 m, the particle's kinetic energy is 20.0 J; at x = 2.00 m, it is 10.0 J. Find c.

Answer 1

c= - 1

Step-by-step explanation:

Given that

F=c x - 3 x²

We know that

Acceleration a

`a=v(dv)/(dx)`

`F=mv(dv)/(dx)=cx-3x^2`

`\int_(v_o)^(v)mv{dv}=\int_(0)^(2)(cx-3x^2)dx`

`\left [m(v^2)/(2)\right ]^v_(v_o)=\left [(cx^2)/(2)-3(x^3)/(3) \right ]^2_0`

`(mv^2)/(2) -(mv_o^2)/(2) =(c* 2^2)/(2)-{2^3}`

10 - 20 = 2c - 8

-10+8 = 2c

c= - 1