For a vehicle moving initially with speed v, its reaction distance is equal to its braking distance. If its speed is increased by 25%, while reaction time and braking acceleration remain unchanged, the ratio of the new total stopping distance to the old one is:
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Question

For a vehicle moving initially with speed v, its reaction distance is equal to its braking distance. If its speed is increased by 25%, while reaction time and braking acceleration remain unchanged, the ratio of the new total stopping distance to the old one is:

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G1 Physics · Accepted Answer

Let the original reaction distance = braking distance = d. Original total stopping distance = 2d. Reaction distance ∝ v, so after increasing speed by 25%: new reaction distance = (5/4)d. Braking distance ∝ v², so new braking distance = (25/16)d. New total = 5d/4 + 25d/16 = 45d/16. Therefore new/old = (45/16)/(2) = 45/32.