AS Daily A Level Physics question
Which statement must be true when a car of fixed mass is brought to rest on level ground by the same steady braking force, but its starting speed is 20% higher than before? (Neglect air resistance.)
Answer
The correct answer is A.
Correct: A — It increases by about 44%. With the same braking force, the stopping distance is proportional to the initial kinetic energy, so s ∝ v^2; raising speed by 1.2 makes s scale by 1.2^2 = 1.44, i.e. a 44% increase. A is correct because it applies the quadratic dependence on speed. B is wrong because it assumes a linear relationship between stopping distance and speed rather than quadratic. C is wrong due to a squaring/miscalculation error (some mistakenly take 1.2^2 as 1.36 instead of 1.44). D is wrong because it suggests an inverse or decreasing trend, which contradicts s ∝ v^2 for constant braking force.