Which of the following braking force statements is untrue?

• A. A vehicle weighing 1500kg will require half the braking force of a 3000kg vehicle
• B. A vehicle weighing 4000kg will require twice the braking force of a 2000kg vehicle
• C. A vehicle travelling 80kph will require four times the braking force of 40kph
• D. A vehicle weighing 4000kg and travelling 50kph will require the same braking force as a vehicle weighing 2000kg and travelling at 100kph

Answer: (D)

The key idea is that the braking force needed to stop in a given distance grows with both mass and the square of speed. If you want to stop in the same distance, the required force is proportional to F ∝ m v^2.

• If speed is the same, halving the mass halves the braking force.

• If mass doubles while speed stays the same, the braking force doubles.

• If you double the speed while keeping the same mass, the braking force quadruples.

For the scenario in question, a 4000 kg vehicle at 50 kph and a 2000 kg vehicle at 100 kph do not require the same braking force. Using F ∝ m v^2: first case is proportional to 4000 × 50^2 = 4000 × 2500 = 10,000,000; second case is 2000 × 100^2 = 2000 × 10000 = 20,000,000. The second requires twice as much braking force, not the same. Therefore the statement comparing these two is untrue.