Question
Which pair of graphs best represents the relationship between velocity, mass and kinetic energy?(1 point)
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GPT-4o mini
In physics, the relationship between kinetic energy (KE), mass (m), and velocity (v) is expressed by the formula:
\[ KE = \frac{1}{2} mv^2 \]
From this equation, we see that:
1. Kinetic energy is directly proportional to mass; as mass increases, kinetic energy increases if velocity is constant.
2. Kinetic energy is proportional to the square of velocity; if velocity increases, kinetic energy increases with the square of that increase.
To represent these relationships graphically:
- If you were to plot kinetic energy (KE) against mass (m) for a constant velocity, the graph would be a straight line, indicating a linear relationship.
- If you plot kinetic energy (KE) against velocity (v), the graph would be a parabola opening upwards (specifically, it would look like a quadratic curve), indicating that as velocity increases, kinetic energy increases much more rapidly.
To summarize, the best pair of graphs to represent the relationship between kinetic energy, mass, and velocity would be:
1. A linear graph of KE vs. m (for a constant v).
2. A quadratic graph of KE vs. v (for a constant m).
If you have specific graph options in mind, please provide them for more tailored guidance.
\[ KE = \frac{1}{2} mv^2 \]
From this equation, we see that:
1. Kinetic energy is directly proportional to mass; as mass increases, kinetic energy increases if velocity is constant.
2. Kinetic energy is proportional to the square of velocity; if velocity increases, kinetic energy increases with the square of that increase.
To represent these relationships graphically:
- If you were to plot kinetic energy (KE) against mass (m) for a constant velocity, the graph would be a straight line, indicating a linear relationship.
- If you plot kinetic energy (KE) against velocity (v), the graph would be a parabola opening upwards (specifically, it would look like a quadratic curve), indicating that as velocity increases, kinetic energy increases much more rapidly.
To summarize, the best pair of graphs to represent the relationship between kinetic energy, mass, and velocity would be:
1. A linear graph of KE vs. m (for a constant v).
2. A quadratic graph of KE vs. v (for a constant m).
If you have specific graph options in mind, please provide them for more tailored guidance.