A block of mass `2 kg` is initially at rest on a horizontal frictionless surface. A horizontal froce `overlineF = (9 -x^(2)) overlinei` newton acts on it, when the block is at `x = 0`. The maximum kinetic energy of the block between `x= 0 m` and `x = 3 m` in joule is
Conservation of mechanical energ

Options

A. 24
B. 20
C. 18
D. 15

Answer

c

Explanation

Kinetic energy , K.E = `int Fdx`
=`overset(3) underset(x=0)int (9-x^(2))dx`
`9 overset(3) underset(x=0)int dx-overset(3) underset(x=0)int x^(2)dx`
`9[x]overset(3)underset(0)-[(x^(3))/(3)]^(3)_(0)=18J`