Question
Which pair of graphs best represents the relationship between velocity, mass and kinetic energy?(1 point)
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GPT-4o mini
To determine the best representation of the relationship between velocity, mass, and kinetic energy, we need to refer to the formula for kinetic energy:
\[ KE = \frac{1}{2} mv^2 \]
where:
- \( KE \) is the kinetic energy,
- \( m \) is the mass,
- \( v \) is the velocity.
From this formula, we can observe that:
- Kinetic energy is directly proportional to mass (\( m \)): If the mass increases, kinetic energy increases, assuming velocity remains constant.
- Kinetic energy is proportional to the square of the velocity (\( v^2 \)): If velocity doubles, the kinetic energy increases by a factor of four (since \( v^2 \) becomes \( 4v^2 \)).
Thus, the graphs that best represent these relationships would show:
1. A linear relationship between kinetic energy and mass when velocity is constant.
2. A parabolic relationship between kinetic energy and velocity when mass is constant.
Please provide the pairs of graphs for further evaluation.
\[ KE = \frac{1}{2} mv^2 \]
where:
- \( KE \) is the kinetic energy,
- \( m \) is the mass,
- \( v \) is the velocity.
From this formula, we can observe that:
- Kinetic energy is directly proportional to mass (\( m \)): If the mass increases, kinetic energy increases, assuming velocity remains constant.
- Kinetic energy is proportional to the square of the velocity (\( v^2 \)): If velocity doubles, the kinetic energy increases by a factor of four (since \( v^2 \) becomes \( 4v^2 \)).
Thus, the graphs that best represent these relationships would show:
1. A linear relationship between kinetic energy and mass when velocity is constant.
2. A parabolic relationship between kinetic energy and velocity when mass is constant.
Please provide the pairs of graphs for further evaluation.