If the weight of a vehicle is doubled, how many times must the braking force be increased to stop the vehicle?

To understand the relationship between the weight of a vehicle and the braking force required to stop it, we can refer to the principles of physics, specifically Newton's second law of motion. This law states that force equals mass multiplied by acceleration (F = m * a).

When the weight of the vehicle is doubled, its mass is also effectively doubled. To bring the vehicle to a stop, the same rate of deceleration must be achieved as it would with the original weight. When mass increases, to maintain the same rate of deceleration, the force applied (in this case, the braking force) must also increase proportionally.

If the original braking force is F, and it’s sufficient to stop the original mass m, when the mass becomes 2m, the braking force required to achieve the same deceleration is 2F. Thus, to stop a vehicle whose weight has doubled, you need to increase the braking force by a factor of two. This is why the correct answer is that the braking force must be increased two times when the vehicle's weight is doubled.

The other options suggest increases by larger factors, which would not align with the direct proportionality dictated by the relationship between mass and force in braking scenarios.