Question

A force Fx=cx-3.00x2 acts on a virus as the virus moves along an x axis, with F measured in Newtons, x in meters, and c a constant. At x = 0, the virus’s kinetic energy is 20.0 J, while at x = 3.00 m, it is 11.0 J. Find c.

Answer 1

4

Step-by-step explanation:

We are given that

`F_x=cx-3x^2`

K.E at x=0 m=20 J

K.E at x=3 m=11 J

We have to find the value of c.

By work energy theorem

Work done=Change in kinetic energy

W=
`\int_(0)^(3) Fdx=\int_(0)^(3)(cx-3x^2)dx`

`W=[(cx^2)/(2)-x^3]^(3)_(0)`

`W=(9c)/(2)-27`

`\Delta K=11-20=-9 J`

`-9=(9c)/(2)-27`

`-9+27=(9c)/(2)`

`18=(9c)/(2)`

`c=(2)/(9)* 18=4`