A varable force, given by the 2- dimensional vector`overlineF=(3xx^(2)hati+4 hatj),` acts on a particle. The force is in newton and x is in metre. What is the change in the kinetic energy of the particle as it moves from the point with coordinates (2,3) to (3,0) (The coornates are in metres)

Options

A. `-7 J`
B. Zero
C. `+7 J `
D. `+19 J`

Answer

C

Explanation

`W=int_(x_i)^(x_f)F(x) dx +int_(y_i)^(y_f) F(y)dy`
`=int_2^3 3x^2 dx +int_(3)^(0)4dy`
`=[x^3]_2^3+[4y]_3^0= (27-8)+(0-12) = 7J`
According to work energy theorem
`DeltaKE = W = 7J`