Question

four vehicles are on the road. rank them from greatest (1) to least (4) kinetic energy.
mass: 4m
velocity: 0
mass: m
velocity: v
mass: 2m
velocity: v
mass: m
velocity: 2v

Explanation:

Step1: Recall Kinetic Energy Formula

The formula for kinetic energy (KE) is \( KE = \frac{1}{2}mv^2 \), where \( m \) is mass and \( v \) is velocity.

Step2: Calculate KE for Each Vehicle

• Vehicle 1 (Mass: \( 4m \), Velocity: \( 0 \)):

Substitute into the formula: \( KE_1 = \frac{1}{2}(4m)(0)^2 = 0 \).

• Vehicle 2 (Mass: \( m \), Velocity: \( v \)):

Substitute: \( KE_2 = \frac{1}{2}(m)(v)^2 = \frac{1}{2}mv^2 \).

• Vehicle 3 (Mass: \( 2m \), Velocity: \( v \)):

Substitute: \( KE_3 = \frac{1}{2}(2m)(v)^2 = mv^2 \).

• Vehicle 4 (Mass: \( m \), Velocity: \( 2v \)):

Substitute: \( KE_4 = \frac{1}{2}(m)(2v)^2 = \frac{1}{2}(m)(4v^2) = 2mv^2 \).

Step3: Rank by KE Magnitude

Compare the calculated KE values:
\( KE_4 = 2mv^2 \) (greatest) > \( KE_3 = mv^2 \) > \( KE_2 = \frac{1}{2}mv^2 \) > \( KE_1 = 0 \) (least).

So the ranking from greatest (1) to least (4) is:

1. Vehicle 4 (Mass: \( m \), Velocity: \( 2v \))
2. Vehicle 3 (Mass: \( 2m \), Velocity: \( v \))
3. Vehicle 2 (Mass: \( m \), Velocity: \( v \))
4. Vehicle 1 (Mass: \( 4m \), Velocity: \( 0 \))

Answer:

1. Mass: \( m \), Velocity: \( 2v \)
2. Mass: \( 2m \), Velocity: \( v \)
3. Mass: \( m \), Velocity: \( v \)
4. Mass: \( 4m \), Velocity: \( 0 \)