In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed v more than that of car B . Both the cars start from rest and travel with constant acceleration a 1 and a 2 respectively. Then v is equal to:

Step-by-step solution

Given, Initially both car is at rest, so u 1 = u 2 = 0 Acceleration of car A   &   B is a 1   &   a 2 Let us assume, Time of reach to destination of car A is, t 1 = t 0 Time of reach to destination of car B is, t 2 = t 0 + t Using second equation of motion, we have u 1 t + 1 2 a 1 t 1 2 = u 2 t + 1 2 a 2 t 2 2 ⇒ 0 × t + 1 2 a 1 t 0 2 = 0 × t + 1 2 a 2 t 0 + t 2 ⇒ a 1 a 2 t 0 = t 0 + t ⇒ t 0 = t a 1 a 2 - 1 From first equation of motion, we have v 1 = a 1 t 0