You might be familiar with Newton’s first law of motion:
“An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.”
This principle, often simplified as “inertia,” is fundamental to understanding motion. It tells us that things tend to keep doing what they’re already doing, whether that’s staying still or moving steadily in a straight line, unless something interferes.
Newton’s First Law and Relative Motion: The Train Example
Imagine you’re inside a train moving at a constant speed on perfectly smooth tracks. The train car is sealed, with no windows to the outside world. Could you tell if you were moving or standing still, just by observing things inside the car?
According to Newton’s first law, you wouldn’t be able to. If you toss a ball straight up in the air, it will come straight back down to your hand, regardless of whether the train is stationary or traveling at hundreds of miles per hour. This is because you, the ball, and the air inside the train are all moving together at the same speed as the train. The only forces acting on the ball, from your perspective within the train, are your hand initially throwing it and gravity pulling it back down.
This concept of relative motion is key to understanding how fast a bullet travels.
Bullet Speed Explained: Relative to What?
Let’s apply this train analogy to a bullet fired from a gun. Suppose a gun fires a bullet at a speed of 1000 mph (approximately 1609 km/h) relative to the gun itself.
If you were to fire this gun while standing still on the ground, the bullet would travel at 1000 mph relative to the ground. Simple enough.
Now, imagine you are on our hypothetical train moving at 1000 mph, and you fire the gun forward in the direction of the train’s movement. The bullet still leaves the gun at 1000 mph relative to you and the gun. However, relative to the ground, the bullet’s speed is now the sum of the bullet’s speed and the train’s speed: 1000 mph + 1000 mph = 2000 mph (approximately 3219 km/h). An observer standing on the ground would see the bullet whizzing by at this much higher speed.
Conversely, if you were to fire the gun backward from the train, in the opposite direction of the train’s motion, the bullet would still leave the gun at 1000 mph relative to you. But in this case, the train’s speed subtracts from the bullet’s speed relative to the ground. So, relative to the ground, the bullet’s speed would be 1000 mph (bullet speed) – 1000 mph (train speed) = 0 mph. In this scenario, an observer on the ground might see the bullet simply drop straight down, as it has no forward velocity relative to their position.
The Speed of Sound: A Crucial Distinction
While bullet speeds are relative and can be added to or subtracted from based on the motion of the shooter, this is not the case for all types of “projectiles.” A prime example of this difference is sound waves.
Sound waves travel through a medium, like air, at a fixed speed known as the speed of sound. In dry air at 20 °C (68 °F), this speed is approximately 767 mph (1234 km/h). Unlike bullets, sound waves cannot exceed this speed in air under normal conditions.
Imagine placing a loudspeaker at the front of our 1000 mph train. If the speaker emits sound waves forward, you might expect them to travel at 1000 mph (train speed) + 767 mph (speed of sound) = 1767 mph relative to the ground. However, this isn’t what happens. Sound waves emanating from the speaker will still travel at approximately 767 mph relative to the air around the speaker, and therefore, roughly 767 mph relative to the ground. They do not gain the added speed of the train.
This fundamental difference explains phenomena like sonic booms. When an aircraft exceeds the speed of sound, it compresses the air in front of it because the air molecules cannot move out of the way quickly enough. This compression creates a shock wave that we hear as a sonic boom. The aircraft itself is moving faster than the sound waves it produces, “outrunning” its own sound.
Conclusion: Understanding Velocity
So, How Fast Does A Bullet Travel? The answer is: it depends on your frame of reference. A bullet’s velocity is relative. It travels at a certain speed relative to the gun firing it, but its speed relative to a stationary observer on the ground can be significantly different if the gun is fired from a moving platform. Understanding this concept of relative velocity, and distinguishing it from the fixed speed of phenomena like sound waves, provides a deeper insight into the physics of motion.
