Answer:
c= - 1
Explanation:
Given that
F=c x - 3 x²
We know that
Acceleration a
[tex]a=v\dfrac{dv}{dx}[/tex]
[tex]F=mv\dfrac{dv}{dx}=cx-3x^2[/tex]
[tex]\int_{v_o}^{v}mv{dv}=\int_{0}^{2}(cx-3x^2)dx[/tex]
[tex]\left [m\dfrac{v^2}{2}\right ]^v_{v_o}=\left [\dfrac{cx^2}{2}-3\dfrac{x^3}{3} \right ]^2_0[/tex]
[tex]\dfrac{mv^2}{2} -\dfrac{mv_o^2}{2} =\dfrac{c\times 2^2}{2}-{2^3}[/tex]
10 - 20 = 2c - 8
-10+8 = 2c
c= - 1
