If a bullet is shot straight up into the air does it achieve the same speed on the way down as it had on the way up at the moment it was fired?
First the answer
If you fire the gun on Earth then no, the bullet comes back down slower than it left.
Now for the physics which explains the answer.
The simplest way to look at this question is probably to use conservation of Energy. You could arrive at the same answer using Newton's laws but it becomes involved. First less us consider firing the gun in a vacuum. The kinetic energy (movement energy) of the bullet when it leaves the gun is gradually converted into gravitational potential energy as it moves up and slows down. Eventually it reaches its highest point and stops. It has zero kinetic energy, all the energy has been converted into gravitational potential. The bullet then starts to fall under gravity. The gravitational potential energy is converted back into kinetic energy. No energy is lost so the bullet arrives back where it started with the same kinetic energy it left with or to put it another way at the same speed it left. If you tried this on Earth it would not happen. The bullet would be subject to air resistance (friction from the air) on the way up. Some of the kinetic energy would be converted into gravitational potential, some would be lost heating the surrounding air. The same would happen on the way down, some energy would be lost. The bullet would arrive back moving more slowly than it left.
An alternate way of looking at it is to use the concept of terminal velocity. It is not as compete from a physics point of view but it may be easier to understand. The bullet, once at the top of the trajectory has no energy left from the gun, all of the energy from that point forward comes from gravity. Any object falling in a gas (like the atmosphere of Earth) can only reach a certain speed, its terminal velocity before the friction from the surrounding gas is equal to the force from gravity. This speed is called terminal velocity. It is determined by the size, shape and mass of an object. The terminal velocity for a bullet is likely significantly less than the muzzle velocity.