On a two lane road, car A is travelling with a speed of `36 km h^(-1)`. Two cars B and C approach car A in opposite directions with a speed of ` 54 km h^(-1)` each. At a certain instant, when the distance AB is equal to AC, both being 1 km, B decides to overtake A before C does, What minimum acceleration of car B is required to avoid an accident?

On a two lane road, car A is travelling with a speed of `36 km h^(-1)`

1.	On a two lane road, car A is travelling with a speed of `36 km h^(-1)`. Two cars B and C approach car A in opposite directions with a speed of ` 54 km h^(-1)` each. At a certain instant, when the distance AB is equal to AC, both being 1 km, B decides to overtake A before C does, What minimum acceleration of car B is required to avoid an accident?
Answer» Velocity of car A, `v_A` = 36 km/h = 10 m/s Velocity of car B, `v_B` = 54 km/h = 15 m/s Velocity of car C, `v_C` = 54 km/h = 15 m/s Relative velocity of car B with respect to car A, `v_(BA) = v_B – v_A` ltbrge 15 – 10 = 5 m/s Relative velocity of car C with respect to car A, `v_(CA) = v_C – (– v_A)` = 15 + 10 = 25 m/s At a certain instance, both cars B and C are at the same distance from car A i.e.,s = 1 km = 1000 m Time taken (t) by car C to cover 1000 m =`1000/25=40s` Hence, to avoid an accident, car B must cover the same distance in a maximum of 40 s. From second equation of motion, minimum acceleration (a) produced by car B can be obtained as: `s=ut+1/2at^2` `1000=5xx40+1/2xxaxx(40)^2` `a=1600/1600=1 m//s^2`

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