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

To solve the problem, we need to calculate the work done on the particle as it moves from the initial coordinates (2m, 3m, 5m) to the final coordinates (3m, 0m, 6m) under the influence of the force \(\vec{F} = (3x \, \text{N}) \hat{i} + (4 \, \text{N}) \hat{j}\).

### Step-by-Step Solution:

1. **Identify the Force Components**:
The force acting on the particle is given as:
\[
\vec{F} = (3x) \hat{i} + (4) \hat{j}
...