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` Joules
B. Zero
C. `+7 J `
D. `+19 J `

Answer

C

Explanation

`Delta K = W= int _(r1 ) ^(r2 ) vecF . D vec r `
` = int _((2,3)) ^((3,0)) ( 3x ^(2) hati + 4 hatj ) . ( dx hati + dyhatj )`
` = 3 int _(2) ^(3) x^(2) dx + 4 int _(3) ^(0) dy = 7 ` joule