Doubling both speed and weight requires how much stopping power compared to the original?

When considering the stopping power required for a vehicle, it's important to understand the physics involved, particularly the relationship between speed, weight, and stopping distance. When both the speed and the weight of a vehicle are doubled, the stopping force required becomes significantly greater.

First, let's break down the factors at play. The stopping distance of a vehicle is influenced by both its speed and its weight. The formula for stopping distance can be simplified to understand how these factors relate:

1. Kinetic Energy: The kinetic energy (KE) of a vehicle is given by the equation ( KE = \frac{1}{2}mv^2 ), where ( m ) is the mass (weight) and ( v ) is the speed. When the speed is doubled, the new kinetic energy becomes four times greater because ( (2v)^2 = 4v^2 ).

2. Stopping Force: In order to stop the vehicle, this kinetic energy must be dissipated. Therefore, if the vehicle's weight is also doubled, the stopping power needed must account for both the increased weight and the increased kinetic energy.

When the weight is doubled, the force needed also doubles. Therefore, combining the effects of doubling both weight