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

Answer:

c= - 1

Explanation:

Given that

F=c x - 3 x²

We know that

Acceleration a

$a=v\dfrac{dv}{dx}$

$F=mv\dfrac{dv}{dx}=cx-3x^2$

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

$\left [m\dfrac{v^2}{2}\right ]^v_{v_o}=\left [\dfrac{cx^2}{2}-3\dfrac{x^3}{3} \right ]^2_0$

$\dfrac{mv^2}{2} -\dfrac{mv_o^2}{2} =\dfrac{c\times 2^2}{2}-{2^3}$

10 - 20 = 2c - 8

-10+8 = 2c

c= - 1