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 a_{1} and a_{2} respectively,the value of v/t is

Sol: If the cars take time t_{1} and t_{2} for the race and their velocities at the end of race be v_{1} and v_{2} , then it is given that

v_{1} – v_{2} =v and t_{2} – t_{1} = 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} $