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A car can produce a maximum acceleration of 5 m/s² and its brakes can produce a maximum retardation of 10 m/s². Assuming the car starts from rest and must come to rest at a destination 1500 m away, find the minimum time (in seconds) to travel this distance.

1. 20 s
2. 25 s
3. 30 s
4. 40 s

Correct answer: 30 s

Solution

Strategy for minimum time: accelerate at full 5 m/s² until reaching peak speed v, then brake at full 10 m/s² until rest. Let t1 = acceleration time, t2 = braking time. Peak speed: v = 5*t1 = 10*t2, so t1 = 2*t2. Distance during acceleration: s1 = (1/2)*5*t1². Distance during braking: s2 = (1/2)*10*t2². Total: s1 + s2 = 1500. Substituting t1 = 2*t2: (1/2)*5*(4*t2²) + (1/2)*10*t2² = 10*t2² + 5*t2² = 15*t2² = 1500. So t2² = 100, t2 = 10 s, t1 = 20 s. Total time = 30 s. Peak speed = 100 m/s = 360 km/h, within the car's capability.

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