When doubling a vehicle's weight, how much stopping power is needed?

When considering the stopping power required for a vehicle, it's essential to understand the relationship between a vehicle's weight and its kinetic energy. The kinetic energy of a moving vehicle is calculated using the formula ( KE = \frac{1}{2} mv^2 ), where ( m ) is the mass of the vehicle and ( v ) is its speed.

When the weight of the vehicle is doubled, the mass in this equation also doubles. Since the kinetic energy is directly proportional to mass, doubling the weight means that the kinetic energy of the vehicle has also doubled. However, to stop the vehicle effectively, you need to consider the work done against that kinetic energy, which is to bring it to a halt.

The stopping force required to counteract this increased kinetic energy is related to the initial kinetic energy. If the mass is doubled, the energy also doubles, and thus, the stopping power—or force applied over a distance to bring the vehicle to a stop—must also be increased accordingly.

Therefore, to stop a vehicle that is twice as heavy at the same speed, you need twice the force to derive that energy for braking. The power doesn’t exponentially increase with weight, but rather in a linear relationship, hence the correct