A physics question

Question

a car is moving with a speed of 15km/h and another car is moving with a speed of 30km/h. compare their kinetic energy

Answer 1

Translational kinetic energy is expressed as: T = (1/2)mv²

In this equation, T is the kinetic energy, m is the mass of the object that is moving, and v is the magnitude of the moving object's velocity (or speed).

We have two cars and were given each car's speed, but we were not given the masses of the vehicles. So we will have these variables:

T₁ = kinetic energy of car 1,

m₁ = the mass of car 1,

v₁ = 15 km/h, which is the speed of car 1,

T₂ = kinetic energy of car 2,

m₂ = the mass of car 2,

v₂ = 30 km/h, which is the speed of car 2.

Because we do not know the masses of the two vehicles, we will have to keep the masses as unknown variables and compare their kinetic energies in terms of those variables.

The kinetic energy of car 1 can be expressed as:

T₁ = (1/2)m₁v₁² = (1/2)m₁(15 km/h)² = (112.5 km²/h²)m_1.

The kinetic energy of car 2 can be expressed as:

T₂ = (1/2)m₂v₂² = (1/2)m₂(30 km/h)² = (450 km²/h²)m₂.

Now, to compare the two kinetic energies, we will find their ratio:

T₁/T₂ = ((112.5 km²/h²)m₁)/((450 km²/h²)m₂) = 0.25 (m₁/m₂) = m₁/(4m₂).

So, the ratio of the kinetic energies gives:

T₁/T₂ = m₁/(4m₂).

Note: Below here is a special case of this problem, and is not the actual answer unless the two cars' masses were in fact the same.

An interesting special case might be whenever the cars have the same mass, or m₁ = m₂, which would give a kinetic energy ratio of:

T₁/T₂ = 1/4.

Which would mean:

T₂ = 4T₁.