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On entering a state highway, a car continues to move with a constant velocity of 6 m s⁻¹ for 2 minutes and then accelerates with a constant acceleration 1 m s⁻² for 6 seconds. Find the displacement of the car on the state highway in the 2 min 6 s time interval by drawing a velocity-time graph for its motion.
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Phase 1 (constant): \(s_1 = 6 \times 120 = 720\ \text{m}\).
Phase 2 (accelerating): \(s_2 = ut + \tfrac{1}{2}at^2 = 6(6) + \tfrac{1}{2}(1)(6^2) = 36 + 18 = 54\ \text{m}\).
Total displacement \(= 720 + 54 = 774\ \text{m}\) (the total area under the velocity-time graph).
