To answer your question effectively, we first need to analyze the data provided in both investigations to understand the relationships between velocity, mass, and kinetic energy.
Investigation 1: Constant Mass
Using the formula for kinetic energy (KE), which is: \[ KE = \frac{1}{2} m v^2 \] Where:
- \( KE \) = kinetic energy in joules
- \( m \) = mass in kilograms
- \( v \) = velocity in meters/second
For the constant mass of 3 kg in Investigation 1:
- Trial 1: \( KE = \frac{1}{2} (3)(8^2) = 96 \) joules
- Trial 2: \( KE = \frac{1}{2} (3)(2^2) = 6 \) joules
- Trial 3: \( KE = \frac{1}{2} (3)(4^2) = 24 \) joules
- Trial 4: \( KE = \frac{1}{2} (3)(6^2) = 54 \) joules
The kinetic energy increases with the square of velocity, meaning it shows a parabolic relationship vs. velocity.
Investigation 2: Constant Velocity
Here, the velocity remains constant (2 m/s), while mass varies:
- Trial 1: For 6 kg, \( KE = \frac{1}{2} (6)(2^2) = 12 \) joules
- Trial 2: For 2 kg, \( KE = \frac{1}{2} (2)(2^2) = 4 \) joules
- Trial 3: For 5 kg, \( KE = \frac{1}{2} (5)(2^2) = 10 \) joules
- Trial 4: For 8 kg, \( KE = \frac{1}{2} (8)(2^2) = 16 \) joules
In this case, kinetic energy increases linearly with mass since the velocity is constant.
Summary of Relationships:
- In the first investigation, kinetic energy is a function of the square of velocity (quadratic relationship).
- In the second investigation, kinetic energy is a linear function of mass.
Graph Selection:
To select the appropriate graphs, you would be looking for:
- A parabola for Investigation 1 (KE vs. Velocity) showing KE increases quadratically with velocity.
- A straight line for Investigation 2 (KE vs. Mass) indicating KE increases linearly as mass increases.
Without seeing the actual graphs A, B, C, and D, I cannot definitively choose which two best represent these relationships, but these principles should help you identify them based on the characteristics we discussed. Look for one graph that has a parabolic shape for the KE vs. Velocity (Investigation 1) and another that has a straight line for the KE vs. Mass (Investigation 2).