A particle starts from rest and travels equal distances in two successive time intervals t₁ and t₂. If the first interval is from 0 to T and the second is from T to t, then t/T equals:
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A particle starts from rest and travels equal distances in two successive time intervals t₁ and t₂. If the first interval is from 0 to T and the second is from T to t, then t/T equals:

G1 Physics · Accepted Answer

From rest under constant acceleration, displacement is proportional to time². Equal distances imply S(T) = S(t) − S(T). Hence T² = t² − T², so t² = 2T² and t/T = √2.