Which statement about braking force is accurate when speed changes?

Which statement about braking force is accurate when speed changes?

• A. If the speed of the vehicle is doubled, the braking force must double
• B. If the speed of the vehicle is doubled, the braking force must quadruple
• C. If the weight of the vehicle is doubled, the braking force must quadruple
• D. If the weight and the speed of the vehicle are doubled, the braking force must be increased by six times

Answer: (C)

Braking force is limited by tire–road grip, which comes from the load on the tires. Heavier vehicles press the tires down harder, so the maximum braking force you can generate increases with weight. The speed you’re traveling, on the other hand, determines how much energy must be removed to stop. Kinetic energy is 1/2 m v^2, so doubling speed means you must dissipate about four times as much energy to stop in the same distance, which makes the required braking force grow quickly with speed. So the key idea is that weight affects how much braking force the tires can produce (more weight → more grip), while speed affects how much energy must be dissipated (higher speed → more energy to remove).

Braking force is limited by tire–road grip, which comes from the load on the tires. Heavier vehicles press the tires down harder, so the maximum braking force you can generate increases with weight. The speed you’re traveling, on the other hand, determines how much energy must be removed to stop. Kinetic energy is 1/2 m v^2, so doubling speed means you must dissipate about four times as much energy to stop in the same distance, which makes the required braking force grow quickly with speed.

So the key idea is that weight affects how much braking force the tires can produce (more weight → more grip), while speed affects how much energy must be dissipated (higher speed → more energy to remove).