A force `vecF=(3xN)hati+(4N)hatj`, with x in meter, acts on a particle, changing only the kinetic energy of the particle. How mcuh work is done on the particle as it moves from coordinates `(2m, 3m, 5m)` to `(3m, 0m, 6m)`? Does the speed of the particle increase, decrease, or remain the same?

Explanation

Given
`barF=(3xN)hati+(4N)hatj`
`W=underset(x_1)overset(x_2)intF_xdx+underset(y_1)overset(y_2)intF_ydy=underset2overset3int3xdx+underset3overset0int4dy`
`=3[x^2/2]_2^3+4[y]_3^0=-4.5J`
As work done in negative, K.E. of the particle will decrease and hence speed will decrease.