A car and a bus are driving along a road at the same speed. The bus has twice the mass of the car. Which vehicle has the greater momentum?

1. Break Down the Problem

To determine which vehicle has greater momentum, we need to understand the relationship between mass, velocity, and momentum. The momentum $p$ of an object is calculated using the formula:

$p = m \cdot v$

where:

• $p$ is momentum,
• $m$ is mass,
• $v$ is velocity.

Both vehicles are stated to be traveling at the same speed.

2. Relevant Concepts

Given:

• Let the mass of the car be $m$.
• Therefore, the mass of the bus will be $2m$ (twice the mass of the car).
• Let the common speed of both vehicles be $v$.

3. Analysis and Detail

Now let's calculate the momentum for each vehicle.

• Momentum of the car:
  $p_{\text{car}} = m \cdot v$

• Momentum of the bus:
  $p_{\text{bus}} = 2m \cdot v$

4. Verify and Summarize

From the calculations:

• The momentum of the car is $m \cdot v$.
• The momentum of the bus is $2m \cdot v = 2(m \cdot v) = 2p_{\text{car}}$.

Final Answer

The bus has greater momentum than the car because its mass is twice that of the car, resulting in:

$p_{\text{bus}} = 2p_{\text{car}}$