Speed and Motion
Problem — How can we measure and describe motion using speed?
- Understand what motion is and how to describe it.
- Learn to define and calculate average speed.
- Connect distance traveled, duration, and speed.
- Use concrete examples to explain the studied concepts.
- Master the scientific vocabulary related to motion and speed.
Part 1: The Concept of Motion
Motion is the change in position of an object or body relative to a given frame of reference, over time.
To say that an object is in motion, you must always specify relative to what this change in position is observed. For example, a passenger in a moving train is stationary relative to the train but moving relative to the outside landscape.
Describing Motion
- The frame of reference: the reference system used to observe the motion (for example, the Earth, a train, a car, etc.).
- The trajectory: the path followed by the moving object within the studied frame of reference (straight line, curve, circle, etc.).
- Displacement: the change in position of the moving object, which can be expressed in distance and direction.
Motion is relative to the chosen frame of reference and corresponds to the change in an object's position over time. Understanding the concept of motion helps to better study movement by specifying the observation frame and the trajectory followed.
Part 2: Speed and Its Characteristics
The speed of a moving object is a quantity that expresses how quickly it changes position: it corresponds to the ratio between the distance traveled and the duration of the trip.
Speed is measured in meters per second (m/s) or kilometers per hour (km/h). It can be constant or vary depending on the motion of the object.
Calculating Average Speed
The average speed v is given by the formula:
v = distance traveled ÷ duration of movement
This gives a general idea of the quickness of a movement even if the actual speed varies during the trip.
Concrete Example
A cyclist travels 12 kilometers in 30 minutes. To calculate their average speed:
- Convert the duration to hours: 30 minutes = 0.5 hours.
- Apply the formula: v = 12 km ÷ 0.5 h = 24 km/h.
Average speed is a simple measure that allows evaluating the overall quickness of a movement. It connects the distance covered and the elapsed time and is easily calculated with the formula v = distance ÷ duration.
Part 3: Relations Between Distance, Duration, and Speed
Distance, duration, and speed are linked by a simple mathematical relationship that allows calculating one of the three quantities if the other two are known.
The basic formula is: v = d ÷ t, where:
- v is the average speed (m/s or km/h),
- d is the distance traveled (m or km),
- t is the duration of the movement (s or h).
We can also write:
- d = v × t (to calculate distance if speed and time are known),
- t = d ÷ v (to calculate duration if distance and speed are known).
Concrete Example
A car travels at an average speed of 90 km/h for 2 hours. What distance has it covered?
- d = v × t = 90 km/h × 2 h = 180 km.
Understanding the relationship between distance, duration, and speed is essential for solving motion problems. With this simple formula, you can easily determine one quantity related to movement when the other two are known.
Part 4: Uniform and Non-Uniform Motion
A motion is called uniform when the speed remains constant throughout the movement. Otherwise, the motion is non-uniform.
In uniform motion, the distance traveled is proportional to time. For example, a car driving at a steady speed on a straight road performs uniform motion.
Concrete Example
If a bicycle travels at 15 km/h for 4 hours without changing speed, it covers:
- d = v × t = 15 km/h × 4 h = 60 km.
On the other hand, if the speed varies because of acceleration or slowing down, the motion is non-uniform and average speed remains a good overall indicator.
Uniform motion is characterized by constant speed, which simplifies calculations of distances and durations. Non-uniform motion is more complex and often requires calculating average speed for analysis.
Part 5: Graphical Representation of Motion
A motion can be represented by a graph plotting distance as a function of time. This representation allows visual study of the object's speed.
Graph Interpretation
- An increasing (rising) straight line indicates motion at constant positive speed.
- A horizontal line means the object is stationary (constant distance).
- A curve indicates non-uniform motion with variable speed.
By calculating the slope of the line between two points on the graph (increase in distance over increase in time), we obtain the average speed over that interval.
Distance-time graphs are valuable tools for analyzing motion. They allow easy visualization of an object's speed and the nature of its movement, helping to deepen understanding.
In this chapter, we discovered that motion is the change of an object's position within a given frame of reference. Speed, which expresses how fast this motion is, links the distance traveled and the duration of the movement. Distinguishing between uniform and non-uniform motion helps in understanding speed variations. Finally, graphical representation provides a visual method for studying these quantities. These concepts are fundamental for approaching many other physics phenomena and form a strong foundation for your future learning.