How can we tell whether an object moves at a constant velocity?
1. The Challenge
According to Newton’s First Law, an object will remain at rest or move with constant velocity unless an external force changes its state. In everyday life, however, it is difficult to find motions that are perfectly uniform.
Often we observe objects that keep the same speed, but not necessarily the same velocity. This happens because velocity includes direction, while speed only indicates how fast something moves.
In this experiment we will observe the motion of a marble inside a tube filled with oil. The resistance of the oil reduces sudden accelerations and allows the marble to reach a motion that is close to constant speed.
The goal is to analyze the relationship between distance and time to determine whether the motion occurs at a constant speed.
2. Real-World Importance
Studying the relationship between distance and time is essential for understanding how objects move. Many natural phenomena can be described using motions that are approximately constant in speed. Examples include:
- The hands of a clock
- The rotation of the Earth
- The motion of certain industrial mechanisms
When an object travels equal distances in equal intervals of time, we say that its speed is constant. This type of analysis allows scientists and engineers to develop mathematical models that describe the motion of vehicles, machines, and natural systems.
3. Mental Model of the Experiment
In this experiment, a marble moves downward through a tube filled with oil. At first, gravity accelerates the marble, but the resistance of the oil opposes the motion. After a short time, these two effects balance each other and the marble begins to move with an almost constant speed.
When this happens:
- The marble travels equal distances
- In equal intervals of time
If we plot the data on a distance–time graph, the points tend to align along a straight line. This indicates that the rate of change between distance and time remains constant.
Speed can be calculated using the relation:Where:
- V = speed
- Δd = change in distance
- Δt = change in time
4. Common Misconception
“If the distance–time graph is a straight line, then the object moves in a straight line.”
In reality, a linear graph does not describe the shape of the path, but rather the relationship between distance and time.
A straight line on the graph means that the object travels equal distances in equal times, which indicates constant speed.
The object could follow different paths in space, but as long as the speed remains constant, the distance–time relationship will remain linear.
5. Expanding the Challenge
By measuring the time it takes the marble to travel each 20 cm segment, you can calculate several instantaneous speeds and then determine the average speed of the motion.
Next, you can construct a graph showing distance traveled as a function of average time.
If the motion is uniform, the experimental points will approximate a straight line that can be described with an equation similar to the one used for a line in mathematics:
Where:
- dᵢ = initial position
- v = constant speed
- t = time
This equation describes the motion of the marble inside the tube and represents a physical model of the observed phenomenon.
6. Scientific Microstory
During the 17th century, Galileo Galilei carried out some of the first systematic studies of motion. To reduce the effects of acceleration, he used inclined planes, which allowed him to observe the motion of a rolling sphere more carefully.
By measuring the distance traveled and the time elapsed, Galileo discovered that the motion of objects could be described mathematically.
These experiments laid the foundations of modern physics and later helped Isaac Newton formulate the laws of motion that we still use today to understand how objects move in nature.
7. Final Question
If simply measuring distance and time allows us to describe the motion of a marble mathematically…
Could we use exactly the same principle to calculate the motion of a car, a satellite, or even a planet?
