Relative speed describes the motion of one object as observed from the perspective of another, whether that other object is stationary or also in motion. It highlights that speed is not an absolute quantity, but rather depends entirely on the observer’s viewpoint. For instance, a car traveling at 60 miles per hour has that speed relative to the road, but its speed relative to a passenger inside the car is zero.
The Concept of Reference Frames
Understanding relative speed begins with the idea of a “frame of reference.” This is the perspective or viewpoint from which motion is observed and measured. All measurements of motion, including speed, are always made in relation to a specific frame of reference.
Changing the frame of reference can significantly alter how we perceive an object’s speed. For example, if you are a passenger on a moving train, the trees outside appear to be moving backward relative to your position. However, for someone standing still on the ground, those same trees are stationary.
When we typically talk about an object’s speed, like a car’s speed, we implicitly use the Earth or the ground as our frame of reference. However, in physics, any object or environment can serve as a reference frame.
How to Calculate Relative Speed
Calculating relative speed depends on the direction in which the objects are moving. There are two primary scenarios to consider: when objects move in the same direction and when they move in opposite directions.
When two objects are moving in the same direction, their relative speed is found by subtracting the speed of the slower object from the speed of the faster object. For instance, if one car is traveling at 60 miles per hour and another car is traveling in the same direction at 50 miles per hour, their relative speed is 10 miles per hour (60 – 50 = 10). This difference represents how quickly the faster car is gaining on the slower one.
Conversely, when two objects are moving in opposite directions, their relative speed is calculated by adding their individual speeds. If a car is moving north at 40 miles per hour and another car is moving south at 30 miles per hour, their relative speed is 70 miles per hour (40 + 30 = 70). This sum indicates how quickly they are approaching each other or moving apart.
Everyday Examples of Relative Speed
Relative speed appears in many everyday situations. One common example involves two cars on a highway. If you are driving at 60 mph and another car passes you going 70 mph in the same direction, that car’s speed relative to your vehicle is 10 mph. If that same car were approaching you from the opposite lane at 70 mph, its speed relative to your car would be a combined 130 mph.
Consider a person walking on a moving escalator. If the escalator is moving upwards at 2 feet per second and you walk up it at 3 feet per second relative to the escalator steps, your speed relative to the ground is 5 feet per second. Conversely, if you walk down the escalator at 3 feet per second while it moves up at 2 feet per second, your net speed relative to the ground would be 1 foot per second downwards.
Another practical illustration is a boat traveling in a river with a current. If a boat moves at 10 mph in still water and the river current flows at 2 mph, the boat’s speed relative to the riverbank changes. When the boat travels downstream with the current, its speed adds up, resulting in a speed of 12 mph relative to the bank. When it travels upstream against the current, its speed is reduced to 8 mph relative to the bank due to the opposing flow.