To analyze the relationship between kinetic energy (KE) and the variables of mass, speed, and time, we can use the formula for kinetic energy:
\[ KE = \frac{1}{2}mv^2 \]
where \( m \) is mass and \( v \) is speed.
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Mass vs. Kinetic Energy: Since kinetic energy increases as mass increases (when speed is constant), a graph of mass vs. kinetic energy would show kinetic energy increasing as mass increases.
- Correct: "a graph of mass vs. kinetic energy, with kinetic energy increasing as mass increases"
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Speed vs. Kinetic Energy: Kinetic energy also increases as speed increases (when mass is constant).
- Correct: "a graph of speed vs. kinetic energy, with kinetic energy increasing as speed increases"
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Time vs. Kinetic Energy: Kinetic energy is not directly related to time in a way that would produce a clear linear or non-linear relationship. Kinetic energy changes as either mass or speed changes, but not straightforwardly with time. Time only affects the velocity (speed) if distance is considered. Hence, there's not a direct correlation presented in the options.
- Incorrect: "a graph of time vs. kinetic energy, with kinetic energy increasing as time increases"
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Speed and Time: The statement regarding speed vs. kinetic energy suggests a contradiction, where kinetic energy may or may not decrease as time increases, depending on external influences like friction and acceleration.
- Incorrect: "a graph of speed vs. kinetic energy, with kinetic energy decreasing as time increases"
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Kinetic Energy and Time with Constant Conditions: If we factor in constant conditions (e.g., constant mass and speed), kinetic energy remains constant over time until conditions change.
In conclusion, the correct graph descriptions based on the relationships are:
- "a graph of mass vs. kinetic energy, with kinetic energy increasing as mass increases"
- "a graph of speed vs. kinetic energy, with kinetic energy increasing as speed increases"