Under the braking force principle, doubling the vehicle speed requires what change in braking force if weight remains constant?

Under the braking force principle, doubling the vehicle speed requires what change in braking force if weight remains constant?

• A. Halve
• B. Quadruple
• C. Double
• D. No change

Answer: (B)

The braking effort needed grows with the energy you have to dissipate, and that energy scales with speed squared. The car’s kinetic energy is (1/2) m v^2, so if you double the speed, the energy to remove becomes four times larger. With constant mass, achieving the same stopping effect (in the same distance or with the same deceleration) requires four times the braking force, since F = m a and a must increase accordingly. Therefore, braking force must quadruple. Halving, doubling, or no change wouldn’t provide enough force to remove the extra energy in the same stopping conditions.

The braking effort needed grows with the energy you have to dissipate, and that energy scales with speed squared. The car’s kinetic energy is (1/2) m v^2, so if you double the speed, the energy to remove becomes four times larger. With constant mass, achieving the same stopping effect (in the same distance or with the same deceleration) requires four times the braking force, since F = m a and a must increase accordingly. Therefore, braking force must quadruple. Halving, doubling, or no change wouldn’t provide enough force to remove the extra energy in the same stopping conditions.