If both the weight and speed of the vehicle are doubled, how many times must the stopping power be increased?

When evaluating the relationship between a vehicle's weight, speed, and stopping power, it's important to understand how these factors affect stopping distance. The stopping power of a vehicle is primarily determined by its weight and its speed at the time of braking.

When both the weight and speed of the vehicle are doubled, the stopping distance will change significantly due to the following reasoning:

• The stopping force required to stop a vehicle is directly related to its weight. Doubling the weight means that the force required to achieve a complete stop also doubles.
• The kinetic energy of a vehicle, which influences the distance it will travel before coming to a stop, is calculated using the formula KE = 1/2 mv^2. If the speed is doubled (2v), the kinetic energy becomes (1/2 m (2v)^2), which simplifies to 2^2 = 4 times the original energy, since mass m is also doubled, this results in an increase in kinetic energy by a factor of 8 (4 for the speed doubling and 2 for the weight doubling).

Therefore, if both the weight and speed are doubled, you would need to increase the stopping power by a factor of 8 to compensate for the increased energy and maintain effective braking