Car accelerates from rest to v, then continues at v for half the acceleration distance. Total time = 30 s. Find v.
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Hint
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Let t₁ be acceleration time. v = a t₁. s₁ = ½ v t₁. s₂ = v (30 - t₁). Given s₂ = ½ s₁? Actually "for a distance equal to half the acceleration distance" means s₂ = ½ s₁. So v(30 - t₁) = ½ × ½ v t₁ = ¼…
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Full Explanation
Let t₁ be acceleration time. v = a t₁. s₁ = ½ v t₁. s₂ = v (30 - t₁). Given s₂ = ½ s₁? Actually "for a distance equal to half the acceleration distance" means s₂ = ½ s₁. So v(30 - t₁) = ½ × ½ v t₁ = ¼ v t₁ → 30 - t₁ = t₁/4 → 120 - 4t₁ = t₁ → 120 = 5t₁ → t₁ = 24 s. Then s₁ = ½ v×24 = 12v, s₂ = v×6 = 6v. So v = at, need a? Also s₁ = ½ a t₁² = ½ a × 576 = 288a. And s₁ = 12v = 12at₁ = 12a×24 = 288a (consistent). So v can be any? Actually v = a×24. No unique v without more info. This problem is under-constrained. Leave as challenge.