To create a line graph showing the relationship between kinetic energy and mass for objects traveling at the same velocity, we first need to understand the formula for kinetic energy (KE):
\[ \text{KE} = \frac{1}{2} mv^2 \]
where:
- \( m \) is the mass of the object,
- \( v \) is the velocity of the object.
Since the velocity is constant for all objects, the kinetic energy is directly proportional to the mass of the objects. This means that as mass increases, the kinetic energy will also increase.
Here’s how the line graph would look:
- X-axis (horizontal): Mass of the objects. This will be marked in equal intervals depending on the masses being measured (e.g., grams or kilograms).
- Y-axis (vertical): Kinetic energy of the objects. This will be marked in equal intervals based on the calculated kinetic energies (e.g., joules).
Graph Appearance:
- Line Shape: The graph would show a straight line that starts from the origin (0,0) and rises linearly. This indicates a direct proportionality between mass and kinetic energy.
- Slope: The slope of the line will be determined by the value of \( \frac{1}{2}v^2 \); since the velocity is constant, the slope will remain consistent throughout the graph.
- Data Points: Each of the four different objects would be represented as a point on the line based on their respective masses and calculated kinetic energies.
Characteristics:
- The graph would not be curved; it would be linear.
- The line will move upwards from left to right, illustrating that as mass increases, kinetic energy also increases.
In summary, a line graph representing the relationship between kinetic energy and mass for objects traveling at the same velocity would show a straight line starting at the origin, reflecting the direct proportionality between mass and kinetic energy.
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