The truck has four times the kinetic energy of the car.
Explanation
Kinetic energy is the energy possessed by an object by virtue of its motion. It is mathematically defined by the formula:
K = ½ mv²
Where m is the mass of the object and v is its velocity.
Analysis:
The problem states that both vehicles move with the same velocity, but their masses differ.
- Let the mass of the car be m and its velocity be v.
- The kinetic energy of the car is: Kcar = ½ mv².
- The mass of the truck is four times that of the car (4m), and it moves with the same velocity v.
- The kinetic energy of the truck is calculated as:
Ktruck = ½ (4m)v²
Ktruck = 4 × (½ mv²)
By substituting the expression for the car's energy, we find:
Ktruck = 4 × Kcar
Therefore, the truck has four times the kinetic energy of the car.
Key Takeaway:
When velocity is constant, kinetic energy is directly proportional to mass. Consequently, if the mass of a body is quadrupled while maintaining the same speed, its kinetic energy also quadruples.