On a two lane road car a is travelling

Asked by admin @ 11/08/2021 in Physics viewed by 312 People

3.8. 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 ?

Answered by admin @ 11/08/2021

Car A is in the middle. Car B and C are on either side of car A. Let car B travel in the same direction as A.

Va = speed of car A = 36 kmph
Vb = - 54 kmph = Vc
Relative velocity of c wrt A : 54+36 = 90 kmph
distance between them = 1 km
time to cross = 1/90 hrs

Initial Relative velocity of car B wrt A : 54 - 36 = 18 kmph
max. Time to cross = 1/90 hrs
Distance : 1 km

s = u t + 1/2 a t²
1 = 18 / 90 + 1/2 * a /90²
a = 2*90 * 72 *1000/(3600*3600) m/s^2
a = 1 m/s^2 or 12,960 km/hour^2

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