The kinetic energy of an object is given by the equation:
KE = (1/2)mv²
where KE represents the kinetic energy, m is the mass of the object, and v is its velocity.
Let's compare the kinetic energies of two cars, one traveling at 10 m/s and the other at 5 m/s.
For the car traveling at 10 m/s, the kinetic energy can be represented as:
KE₁ = (1/2)m(10)² = 50m
For the car traveling at 5 m/s, the kinetic energy can be represented as:
KE₂ = (1/2)m(5)² = 12.5m
We are given that the kinetic energy of the first car is four times the kinetic energy of the second car. Mathematically, we can express this as:
KE₁ = 4KE₂
Substituting the expressions for kinetic energy derived earlier, we have:
50m = 4(12.5m)
Simplifying the equation:
50m = 50m
The mass (m) cancels out on both sides of the equation, which means that the mass does not affect the comparison of kinetic energies in this scenario. Therefore, we can conclude that the kinetic energy of the car traveling at 10 m/s is four times the kinetic energy of the car traveling at 5 m/s simply because the kinetic energy is directly proportional to the square of the velocity.