Question

Question 2 (1 point)
Tyana is using lead balls to perform investigations of kinetic energy. She records her observations in two tables.


INVESTIGATION 1: constant mass
Trial Velocity (meters/second) Mass (kilograms) Kinetic Energy (joules)
1 8 3 96
2 2 3 6
3 4 3 24
4 6 3 54


INVESTIGATION 2: constant velocity
Trial Velocity (meters/second) Mass (kilograms) Kinetic Energy (joules)
1 2 6 12
2 2 2 4
3 2 5 10
4 2 8 16

Using the patterns observed in Tyana's data, which two graphs best represent the relationships between velocity, mass, and kinetic energy?

a. M1Q1a_6837450d8d87d.JPG

b.

c.

d.

a
d
b
c
c
a
d
b
English

Answer 1

To determine which two graphs best represent the relationships between velocity, mass, and kinetic energy based on Tyana's data, we need to consider the relationships expressed in the kinetic energy formula:

\[ KE = \frac{1}{2} mv^2 \]

Where:
- \( KE \) is the kinetic energy,
- \( m \) is the mass, and
- \( v \) is the velocity.

### Investigation 1: Constant Mass
In this case, mass is constant (3 kg) and the kinetic energy varies with the square of the velocity:
- When \( v \) is 2 m/s, \( KE = 6 \) J
- When \( v \) is 4 m/s, \( KE = 24 \) J
- When \( v \) is 6 m/s, \( KE = 54 \) J
- When \( v \) is 8 m/s, \( KE = 96 \) J

This indicates a quadratic relationship between velocity and kinetic energy.

### Investigation 2: Constant Velocity
In this scenario, velocity is constant (2 m/s), and the kinetic energy varies with mass:
- When \( m = 2 \) kg, \( KE = 4 \) J
- When \( m = 5 \) kg, \( KE = 10 \) J
- When \( m = 6 \) kg, \( KE = 12 \) J
- When \( m = 8 \) kg, \( KE = 16 \) J

This indicates a linear relationship between mass and kinetic energy.

### Choosing Graphs
1. For Investigation 1, you want a graph that shows a squared relationship (quadratic) between velocity and kinetic energy.
2. For Investigation 2, you want a graph that represents a linear relationship between mass and kinetic energy.

Without seeing the specific graphs provided, you'll have to pick one that has a parabola shape representing the quadratic relationship for Investigation 1 and one that shows a straight line for Investigation 2.

Therefore, based on this reasoning, you'll want to look for:
- A quadratic graph for Investigation 1,
- A linear graph for Investigation 2.

If you can reference the specific graphs labeled a, b, c, and d, look for one that matches these descriptions!