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Motion in a straight Line
on a two lane road car a is travelling with a spe...

Question:
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_x = 36 km/h = 10 m/s

Velocity of car B, v_y = 54 km/h = 15 m/s

Velocity of car C, v_z = 54 km/h = 15 m/s

Relative velocity of car B with respect to car A,

v_yx = v_y – v_x = 15 – 10 = 5 m/s

Relative velocity of car C with respect to car A,

v_zx = v_z – (– v_z) = 15 + 10 = 25 m/s

At a certain dinstance, 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 + ½ at²

1000 = 5 x 40 + ½ x a x 40²

a = 1600 / 1600 = 1 m/s²

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