In a car race, car A takes time t less than car B and passes the finishing point with a velocity v more than velocity…

Q: In a car race, car A takes time t less than car B and passes the finishing point with a velocity v more than velocity with which car B passes the point. Assuming that the car starts from rest and travel with constant
acceleration a1 and a2 respectively,the value of v/t is

Sol: If the cars take time t1 and t2 for the race and their velocities at the end of race be v1 and v2 , then it is given that

v1 – v2 =v and t2 – t1 = t

$\large \frac{v}{t} = \frac{v_1 – v_2}{t_2 – t_1} $

$\large \frac{v}{t} = \frac{\sqrt{2 a_1 s} – \sqrt{2a_2 s}}{\sqrt{\frac{2s}{a_2}} – \sqrt{\frac{2s}{a_1}}} $

$\large \frac{v}{t} = \frac{\sqrt{a_1 } – \sqrt{a_2}}{\sqrt{\frac{1}{a_2}} – \sqrt{\frac{1}{a_1}}} $

$\large \frac{v}{t} = \sqrt{a_1 a_2} $