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A particle moves with displacement x = 2t³ - 15t² + 36t (x in metres, t in seconds) starting at t = 0. List-I (P) Magnitude of displacement at t = 2 s (in m) (Q) Distance travelled from t = 0 to t = 2 s (in m) (R) Speed of the particle at t = 5 s (in m/s) (S) Acceleration of the particle at t = 5 s (in m/s²) List-II (1) 36 (2) 28 (3) 30 (4) 32
- P -> 2; Q -> 2; R -> 1; S -> 3
- P -> 2; Q -> 4; R -> 3; S -> 1
- P -> 3; Q -> 2; R -> 3; S -> 1
- P -> 3; Q -> 4; R -> 3; S -> 1
Correct answer: P -> 2; Q -> 2; R -> 1; S -> 3
Solution
v = 6t² - 30t + 36 = 6(t-2)(t-3). v > 0 for t < 2, so particle moves only forward during [0,2]. x(0) = 0, x(2) = 28 m. P = 28 m (List-II 2), Q = 28 m (List-II 2). v(5) = 6*25 - 150 + 36 = 36 m/s (List-II 1). a = 12t - 30; a(5) = 60 - 30 = 30 m/s² (List-II 3).
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