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Difficulty: MediumMomentum and Collisions

Momentum is defined as the product of an object's mass and its velocity (p=mvp = mv). Arrange the following vehicles in order of their total momentum, from the lowest to the highest.

  1. 1A 400 kg400 \text{ kg} motorcycle traveling at 25 m/s25 \text{ m/s}
  2. 2A 5,000 kg5,000 \text{ kg} bus traveling at 5 m/s5 \text{ m/s}
  3. 3A 1,500 kg1,500 \text{ kg} car traveling at 20 m/s20 \text{ m/s}
  4. 4A 3,000 kg3,000 \text{ kg} truck traveling at 12 m/s12 \text{ m/s}

Answer

The correct sequence from lowest to highest momentum is: motorcycle, bus, car, and finally the truck.
The correct sequence is found by multiplying each vehicle's mass by its velocity and then ordering the products from smallest to largest: motorcycle (10,00010,000), bus (25,00025,000), car (30,00030,000), and truck (36,00036,000).

Step-by-Step Solution

1
Recall the formula for calculating momentum.
p=m×vp = m \times v
Momentum requires multiplying the mass of the object by its velocity.
2
Calculate the momentum for the motorcycle.
400 kg×25 m/s=10,000 kg⋅m/s400 \text{ kg} \times 25 \text{ m/s} = 10,000 \text{ kg}\cdot\text{m/s}
This establishes the total momentum for the first vehicle.
3
Calculate the momentum for the bus.
5,000 kg×5 m/s=25,000 kg⋅m/s5,000 \text{ kg} \times 5 \text{ m/s} = 25,000 \text{ kg}\cdot\text{m/s}
This establishes the total momentum for the second vehicle.
4
Calculate the momentum for the car.
1,500 kg×20 m/s=30,000 kg⋅m/s1,500 \text{ kg} \times 20 \text{ m/s} = 30,000 \text{ kg}\cdot\text{m/s}
This establishes the total momentum for the third vehicle.
5
Calculate the momentum for the truck.
3,000 kg×12 m/s=36,000 kg⋅m/s3,000 \text{ kg} \times 12 \text{ m/s} = 36,000 \text{ kg}\cdot\text{m/s}
This establishes the total momentum for the fourth vehicle.
6
Order the resulting values from lowest to highest.
10,000<25,000<30,000<36,00010,000 < 25,000 < 30,000 < 36,000
The question requires arranging the vehicles in ascending order based on their momentum.

Key Concept

The total momentum of a moving object is directly proportional to both its mass and its velocity.
Estimated Time:1m 0s
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Topics

Momentum and Collisions

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