If the weight of a vehicle doubles, how does this affect its kinetic energy?

Kinetic energy is given by the formula ( KE = \frac{1}{2}mv^2 ), where ( m ) is the mass of the object and ( v ) is its velocity. When the weight of a vehicle doubles, it directly impacts the mass in the kinetic energy equation. The doubling of the mass means that in the equation, ( m ) is now ( 2m ). Plugging this into the kinetic energy formula, we have:

[ KE = \frac{1}{2}(2m)v^2 = mv^2. ]

Now, while the term for mass has increased, the velocity ( v ) remains the same, meaning that the kinetic energy effectively doubles as a result of the increased mass.

Additionally, if the velocity is also considered to double alongside the mass, the kinetic energy expression becomes:

[ KE = \frac{1}{2}(2m)(2v)^2 = \frac{1}{2}(2m)(4v^2) = 4mv^2. ]

In this scenario, the kinetic energy quadruples due to the square effect of the velocity. Therefore, if both mass doubles and velocity doubles, the kinetic energy indeed quadruples