On a two lane road, car A is travelling with a speed of 10 m/s and other two cars B and C approach car A in opposite directions with a speed of 15 m/s. At an instant, when the distance A B is equal to

Question

On a two lane road, car A is travelling with a speed of 10 m/s and other two cars B and C approach car A in opposite directions with a speed of 15 m/s. At an instant, when the distance A B is equal to A C , both being 1 km, B decides to overtake A before C does. What minimum acceleration of car B is required to avoid an accident?

TestHub · Accepted Answer

C closes on A at 15 + 10 = 25 m / s , reaching A in t = 25 1000 ​ = 40 s . B (behind A , same direction) must cover the 1 km gap within 40 s; relative to A its initial speed is 15 − 10 = 5 m / s : 1000 = 5 × 40 + 2 1 ​ a ( 40 ) 2 gives 800 = 800 a , a = 1 m / s 2 . Matches the printed answer.

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