using newtons 2 nd law of motion , a rocket fired towards ,neptune?

If you fired the thrusters at the correct time, yes. The idea for saving fuel is a hohmann transfer orbit, which uses a lot of fuel to reach the escape velocity for the Earth. Then you are basically orbiting the Sun at the same distance the Earth is. If you accelerate that object enough, at one point in that orbit, that point becomes the perihelion of the spacecrafts new orbit, and if your calculations were correct, the orbit of Neptune, on the other side of the Sun, would be your crafts aphelion point. If you time it well, you won't need to make many course adjustments.

Of course, you would have to use your thrusters again when arriving at Neptune if you wished to orbit it.

Any flight faster than a Hohmann would require more fuel usage.

A lot depends on the final velocity of the rocket when it left Earth's gravity field, don't you think.

Some trajectories could use other planets to "slingshot" the rocket towards Neptune, but that requires rocket and planet(s) to be in the right place(s) at the right time(s).

Look up the New Horizons probe heading for Pluto and how it was "shot" --- very interesting.

www.nasa.gov/mission_pages/newhorizons/main/index.html

Yes it would have to use fuel. If it has to be steered it will need fuel to operate the retro rockets. There is a lot of planning and mathamatics put into planning a fete like this since the object in question is never near where it will be when the space craft gets to it's locality in space.

You would only need fuel to escape the gravitational pull of a celestial object. Once you leave the gravity of a celestial object, you will stay at the constant speed in which you left, so you won't need any fuel. (If you left at 5000km/hr, you would keep going at 5000km/hr without fuel consumption.)