A force `F = Ay^(2)+By+C` acts on a body at rest in the `Y`-direction. The kinetic energy of the body during a displacement `y = -a` to `y = a` is

Options

A. `(2 A a^(3))/3`
B. `(2A a^(3))/3+2 Ca`
C. `(2 A a^(3))/3+(Ba^(2))/2+Ca`
D. None of the above

Answer

B

Explanation

`W=int_(-a)^(+a) F dy=[(Ay^(3))/3+(By^(2))/2+Cy]_(-a)^(+a)=(2Aa^(3))/3+2Ca`